Can I deduct work - to - school and vice versa commute?

Your advisor was right. You cannot deduct commuting miles.

The IRS defines your commute as “transportation between your home and your main or regular place of work.” Your “home” is the place where you reside.

Okay. But how about school to work and work to school ?

School is not a place of work. And that would count as commute too.

I found an article that claims: "Business education: If you’re taking courses at a local college to improve your job skills, you may usually go straight to school after work on weekdays. The cost of the travel between work and the school is deductible (or between school and work if you’re taking a morning class)."