It took me all summer last year to get the Sikkins off, pretty much the same as varnish, and yes it was pealing. I used a heat gun and scraper. Real shitty job to have to do. Oil is the only way to go.Teak is very oily wood and refuses to bond with most varnish finishes. Teak oil is easier to apply and looks better.
I bought a sailboat 4 years ago that someone had "painted" the brightwork with varnish. All of it has peeled off the first year.
I have always used oil.