"since last year" and "for the last year"

Question

I'm having trouble explaining the sentence below to my student. He thinks the definite article has something to do with his rationale for using "for" instead of "since".

Skateboarding can be dangerous. Since the 1960s, thousands of people have gone to hospital emergency rooms because of injuries.

I understand the answer in the sentence above is "since". Considering the constructions below however, he asked why "for" can't also be used.

I have lived in Austin since last year. I have lived in Austin for the last year.

Can someone help?

Answer 1

Since last year = since 2019.

For the last year = during the previous 12 months.

Since is used in relation to a specific date or period in the past (yesterday, last year, the 1960s). For is used of a length of time (a while, an hour, the past week).