Well, I hate the "BLANKET" statement that owner - non-horse person - made.
I have seen halters grown into a horses face and head (and the dog collars too - gak!!). I've seen them get caught in fencing and with their legs while scratching. I've seen a horse get a shoe caught in woven wire, straight wire and WOOD fencing (that one tore his hoof apart trying to get loose - the farrier and vet bills for that owner who insisted the shoe wasn't loose enuf to warrant a phone call to the farrier & time off from work - well I learned my lesson when I was in my teens!).
I don't like leaving halters on. Our ponies rub constantly - sometimes just to rub, sometimes due to flies and this year - GNATS are terrible. I'm watching 4 young mares as I type this - all in the same pasture rubbing in different areas of the pasture (one on her front leg). Honestly, mine are difficult to leave halters on - they rub them off (or could/would get hung up).
I DO leave collars on them. I've now done this for 17 years - could they get caught? MAYBE, POSSIBLY, YES. I have yet to see the foals get caught, I have yet to see anyone else get caught. I either make or purchase the collar with the intention of it not breaking - but have had some break when I haven't replaced them soon enuf (the braided haystring ones wear out and the nylon dog collars shrink in weather - just like halters do). We are currently on 9 acres BUT our road has become a major connection between two highways one of which has the emergency center on. Trees have come down on our pasture fences, ponies have run thru hot/woven fencing, and wood boards have been either knocked out or broken when a more aggressive pony has chased one into/thru the fence - with collars on they have have been catchable for someone on the road - with ID attached w/ our phone numbers and the ponies' names. Right now - most of my collar markers have faded - I'm getting ready to do another batch for EVERYONE before I leave and have all the "tan" ponies cared for by someone else over 4th of July weekend.
I used to agree that catching was always a "training thing". HOWEVER, I have worked with horses and ponies of specific bloodlines in TWH, QH, PH, Apps, Morgans, Arabs, Hackneys AND Shetlands (I don't work/really haven't owned "true" mini horses) that are notorious for being both hard to catch and hard to handle over the years. years ago, those type horses were known as "for experienced handlers only" or "not beginner horses" or "not a kids' pony". People getting into horses these days have bleeding hearts that seem to think every horse is easy and handle-able by anyone - I will never believe that!! I have seen it and HAVE IT RIGHT NOW ON MY PROPERTY run in bloodlines. I have a mare from a well known, "kid pony" line from a respected breeding farm. LOVE her but she's a pain in the neck - to catch, to handle her head and ears. NO AMOUNT of constant desensitizing helps but I don't drug her. Her oldest daughter has spent two years with a trainer and done well as our FIRST show pony from our breeding program. She was handled daily from birth to the day she went to the trainer. Don't know what she had done specifically at the trainers - but they DID "coo" over her except at clipping time. Now she's back home and is a pasture pony again - can't catch her in the open w/o running her into the round pen and CAN NOT handle her head/ears. She gets them handled 2x daily - wears a fly mask that goes on in the AM and off in the PM. Her two "baby" sisters are exactly the same way - right from birth! Hard to catch, not really freindly, HATE having their heads and ears touched. I deal with it - I like them, I personally like their bloodlines. The last one - was a born biter. I watch her and keep a good hold on her when the farrier works on her hooves. Her eyes change colors right before she opens her mouth and dives. My farrier knows I will snatch and correct her - she's getting better. She did this right from her first hoof trim at 30 days of age. She just turned a year old. She's not for sale and I wouldn't "foist" her off on an unsuspecting handler w/o warning and/or proper instruction.
Again - have another mare from a long established mid-western breeding program. She ran on pasture first at one farm and then at another before I purchased her. Then I was warned about ponies of her "bloodlines"... She's not easy to catch. I now suspect she was run thru a chute to halter and load her on the transport trailer. She arrived in foal at our place, upset and untouchable. She ended up foaling early and for the three days the colt lived, I was able to catch and touch her - milked her, introduced her son to her, got him to nurse and I literally went nuts touching and rubbing her every chance I got for those 3 days (took 2 vacation days to stay home with her). Suspect the colt was a "dummy foal" - had the symptoms but died before our vet could see him. I didn't send him for necropsy - mare went stark, raving mad! Took a couple of days before we could get into her paddock to remove the colt. When we did - we buried him and actually led her to the burial site (WOW). She's lives in a double round pen situation inside of a double fenced pasture of about 1 acre. The one time she was turned out - she blew thru not only our fences but several neighboring farms' as well. Took 9 people - in trucks, on horseback and ATVs - 2 highways, several tobacco and soybean fields and TEN MILES away - got her turned around and headed back for home. Have no idea how we actually herded her back into OUR barn (the other ponies?) - but we did and cornered her and caught her. She wasn't injured (she was sore in the legs - deep sand in two of the tobacco fields and a whole lot of miles mostly at a gallop or good long trot!). We peeps were more tired at that point than she was. The $$ I paid for repairs to fencing and owners' fields - yikes!!! She's turned into one VERY EXPENSIVE pony and that was a Mother's Day that will never be forgotten!!! I've talked to a number of trainers in our "area" - some up to 250 miles away. Several have flat turned down training/working with her and some have said they'd more than double what they normally charge - some were natural horsemanship type and some were/are more cowboy/old school type. Two - after studying her and working with her for 1/2 an hour said she'd be one better in the ground. In May, my hours were cut back and I've gone back to working with her myself. I can't catch her easily, can't touch her head or ears (can touch her muzzle and between her eyes) but yesterday with a loose line to her neck, I was able to pick up and hold all 4 hooves. She has been wormed (well it's been a while now) but hasn't had a coggins test or any vaccinations and this is the first time I've been able to handle her hooves in the two years since she arrived. She has 8 young mares in the pasture she's penned in and every now and then I will turn one in with her when she appears to be "pining" for friendship/scratches. It has worked well enough. Her personality is disappointing - her grand dam is a much loved pony and one of the best equines I've ever owned OF ANY BREED. Her grand dam is part of the reason I wanted her. I also have purchased several other ponies with similar/same bloodlines - they all have "quirks" about being caught and handled! Just like us - they have good and bad days - 4 mares and a gelding - three were purchased as weanlings and handled daily from then on. They all drive - single and pairs - but are "difficult". None would be considered to be beginner ponies...
Back to the OP's original observation - the FB post shows a lack of knowledge and horsemanship, IMHO. So many of the newbies that I find getting into horses now LACK basic horsemanship skills and have no desire to learn them. Nor do they want to be told that they should. I've seen it here in NC with folks purchasing full size horses - but it's most noticeable with MH purchasers who seem to want a "big dog"... And later, in talking with some who didn't want to learn horsemanship skills - they no longer own horses. "Too much work" is what I've been told.
:rofl