During my last decade or so of classroom teaching, I wore a long-sleeved shirt and tie almost every day. Much of that time I was the only male teacher on campus to do so. I taught History and Computer classes, not wood- and metalshop as I had earlier in my career, and did not worry about getting dirty or getting caught up in machinery.
My dad wore a tie, most of my male teachers in high school and college wore ties, so I wore one too. If you expect to be paid and treated like a professional, you should dress like one.
But ties don’t have to be the boring, formal ties you see on politicians and lawyers. There is a lot of room for imagination and tweaking your nose at the system. A lot of “character” ties exist and now you can design your own and have them economically produced online and by mail order.
When I retired I had a collection of several dozen such ties; enough of them that using only those ties one of my students in a year long class would only see it three times and a student in a trimester class would only see it once.
I saw, and still see, too many men who look uncomfortable in ties. Their shirts are too small or, at least their collar size is too small. Always buy shirts with a collar size one-half inch too large. If you have a sixteen inch neck, buy a shirt with a sixteen and one-half inch neck. You’ll always be comfortable wearing a tie, and, if you gain a little weight, it’ll still fit.