So much has been written on this topic, but
@Tyson really nailed it succinctly. This is a controversial subject for many, but it really shouldn't be for Mustachians, particularly for US based followers.
I can't pay off my mortgage with pre-tax dollars. But I CAN invest in my 401k with pretax dollars. That alone is a no brainer for the $18k that I can into a 401k every year. The fact that I get an employer match for another $6k to get to $24k per year makes it a double no brainer.
Add to that the fact that my investments yield an average of 8% return over the long term and paying the mortgage only nets me 3.9% and it's a triple no brainer!
For the record, I have nothing against living mortgage-free, as long as one chooses the most optimal method of achieving that. It's pretty counter-intuitive, but so is the entire concept of FIRE. The benefit of understanding this math is huge, especially for those who aspire to FI and RE as efficiently as possible.