If 80% to 90% of people lose money day trading, how is it a profession?

In the same way that 90% of boxers will never turn pro, and of those that will, only a small number will make millions.

In the same way that most people playing high school ball will never play in the NBA.

Trading is a difficult thing to learn, and a difficult skill to perform consistently at. It CAN be learned like any skill, through focused and intelligent practice. The problem is a thing called the Dunning-Kruger effect, which is basically that when you get a little bit of skill you actually think you are really good. When I’d been trading for 3 years I thought I was a rockstar, but in reality I still sucked.

It is just like learning to be a concert pianist, or a world class chess player, or anything really hard.

How much does the average day trader make per day?

The average, if you added all the day traders total profit and divided by the number of traders would be a small negative number.
Never forget this. An average scientist becomes a teacher. An average basketball player becomes a high school coach.

An average trader goes broke.

Is day trading a loser’s game?

For the overwhelming majority of people yes. Day trading is harder, by definition, than longer term trading as the decisions are made faster under greater pressure.

To day trade successfully in the long term you have to be truly expert, just “better than average” is a recipe for disaster.

Do you have to be good at calculus, statistics, and other complex subjects to be a good day trader?

No. You need to leverage your strengths, and if your strengths were advanced maths you could find a way to build a method that did that. In the same way as if your strength was programming you could find a way to leverage that.

My experience is that the maths involved in trading rarely gets much more complicated than the functions in an excel sheet, though if you trade options this is no longer true.