how to convince parents to let me switch my major from engineering

What other careers are OK for your parents if you aren’t an engineer? Start with that.

What kind of part-time jobs have you had in high school or so far in college? Are those dead ends or can they lead to something better? What kinds of paid internships can your college career center help you find for you possible other major(s) that could lead to a job after graduation?

What can you envision yourself doing if you don’t end up in law school? What kind of job do you think you’d like?