Risk, I think. For most people this is a higher risk strategy long term than just "paying the mortgage". Depending on your life stage and overall position it can make sense but it's not for everyone.
A lot of the talk about how great mortgages were has the benefit of hindsight. Yes, if you have steady income, it would have been better to get a larger mortgage a couple years ago when money was cheaper (assuming you bought in an area that appreciates, assuming maintenance isn't crazy, assuming you aren't overly leveraged). You have to make several qualifying statements.
It's literally lower risk to invest if your average investment return rate is lower than your mortgage rate. It's likely more of a psychological opposition, where people want to feel more secure with a fully paid off mortgage, even if it does lose them potentially millions in the course of their lifetime.
It's impossible to average 5% return risk-free (if mortgage interest is 2% or whatever). Saying "as long as your average return is higher than your mortgage interest then it's lower risk" is a ridiculous statement, the entire reason you're getting a better return is because you're taking on more risk.
