Is it worth DIY remove old tiles or just put new tiles on old tiles in Kitchen?
It depends.

If the current tiles are intact but unfashionable, and if you have enough room above the floor and under the door for new tile, it's easier (read: cheaper) to lay on top. This is usually feasible for most types of actual tile, old and new. Linoleum (not tile), high-gloss tiles (ex subway), and non-ceramic tiles (ex parkay) often don't make suitable underlayment, so they can't be used regardless of the condition they are in.

If the current tiles are broken, missing, crooked, etc, then they need removed for two main reasons: 1. they won't provide a flat stable surface for new tiles. 2. They are probably hiding a sub-floor problem like leaks, joist sagging/warping, rot, insects, mold, etc that should be addressed before doing a new floor anyway.