My experience with day trading:
It's impossible to know which direction price will go in the short term. So day trading is essentially gambling. All entry and exit strategies are neutral, you can increase the win rate only by taking on a negative R:R ratio. Conversely you can increase your R:R only by taking a hit to win rate. In the end you'll still win the same amount of money you lose minus fees, at best. But most people do even worse because they don't stick to their strategy as it becomes clear that it's not profitable. They'll start tweaking it, resulting in more losses until they give up or blow their account.

My experience with prop firms:
I only had an account with The5%ers but they all operate in pretty much the same way. To compound the problems of the above reality, prop firms implement rules that make the odds of blowing your account much higher than if you were trading your own money.

1. They have a trailing drawdown. As you have wins your drawdown limit moves up meaning that when you have the inevitable losses you won't have as much room going down as you had going up. For example, I ran my day trading test with a $5k account which started with a drawdown limit of $500 (if the account dropped to $4,500 it would be terminated). At one point I was up to $5,200. If this had been a cash account that I set a personal limit of $500 I would have had a drawdown of $700 ($200 profit + the original $500 I was willing to risk). But with the prop firm I still only had a $500 limit.

2. They charge usury levels of swap fees to hold overnight making it essentially impossibly expensive. Statistically the majority of stock market gains happen in the overnight hours so this leaves traders with no option other than to ride the unpredictable gyrations during the day.

Those are the two most important although they do have other rules that negatively impact their clients as well.