Over the years I have seen many wonderful horse and rider combinations, I have also seen the entirely wrong pairing. Much like any relationship, not everyone is a good match for each other. When you have been riding for years you can work with most horses but for beginners or even the intermediate rider many horse are just not appropriate. I see many people buy a particular horse because it's affordable, the look they are going for or because they didn't listen to a knowledgeable person. Many trainers don't know how to match their students and they pair their student with the wrong horse and within weeks or months their student loses their nerve and quit or become terrified or riding this horse they just bought. There are many schoolmasters that are not even given a look because the beginner rider wants the fancy flashy younger model that in reality needs a professional rider. If you want to learn to ride well, first you need to ride a horse that has been there and done that so you can focus on yourself. It's very hard as a beginner or intermediate rider to sit on a green horse and be successful, I have seen it done but it is very rare and the horse is something quite special.
With OTTB's or baby warmbloods being so affordable and gorgeous it is very tempting to rush out and buy one, but I would rather find a been there done that older horse that knows the ropes and can teach my students how to ride well, rather than how to not die. Leasing is another great option, especially if you are moving up the levels at a rapid pace. Green horses that are matched with inexperienced riders wind up stopping, bolting, rearing, terrible ground manners and sometimes so dangerous they need to be destroyed or sent off for thousands, if not 10s of thousands of dollars to fix. I witnessed just that about 20 years ago, a young girl didn't have much money and she went to an auction and bought a 17.2 chestnut with a large white blaze and 4 gorgeous white socks, he was breathtaking. She didn't handle him well, so he started bullying her, biting, dragging her and one time she got her hand caught in the lead rope and he took off and tore off one of her fingers. She tried riding him and within a few weeks he started rearing and bolting with her and she became terrified of him and rightfully so. She realized she needed help so I was tasked with making him safe. It took months of working with him and over a year before he was safe for her to ride him. The money she saved buying a cheap horse cost her more in training in the end. She would have been better suited buying or leasing a suitable horse. In the end she wound up with a nice horse that was dependable and her son was able to learn to ride on him, but I have also seen this end up where the horse reared up, flipped over and crushed the man and the horse broke his neck and was euthanized. This could have been prevented with a little common sense and an experienced horseman to aid in your search. And when they suggest the quiet, older packer buy or lease that one so that one day you can buy the younger flashy one and you will have the skills to train it yourself. One of my riding buddies when I was a teen didn't have the most money and she was an excellent equitation rider, her trainer found her an ex grand prix horse that had an old injury that kept him from jumping much about 3'6 but with the right maintenance and care he packed her around and those two won some large medal classes over the years, she wound up with a horse that had once cost 6 figures for a song and had an amazing partner that she learned more from than any other horse she owned. In the end if you are training with someone you need to respect them and trust them to help you find the correct horse, but know that not every trainer has your best interest and some don't want to do the leg work to find "the one" and if that is the case it is time to find a new trainer.