It has taken me many years of patiently peeling ivy from my trees to discover the best way to do it. The obvious way, prising part of the woody stem from the bark and pulling, only results in broken ivy and the chore of chipping off the fragments.
The technique: detach just enough of the ivy to get your hand round it (or for young stems your fingers) and pull it upwards, (or downwards), parallel to the tree. The little pads it uses to cling with can resist an outward pull, but not a pull in the direction they are growing, or have grown.
Spring, while they are growing, is the time to do it. Let no one persuade you ivy is good for trees, or looks anything but slovenly on them.