We aren't worried about regime change per se.
We are worried about the escalation of a conflict that has so far proved a humanitarian disaster (and could almost certainly have been prevented in its current form if certain non-violent methods had been used earlier but it's too late for that now). Much of the fragmentation of the opposition and attendant bitterness and extremism is born out of a feeling that they've been let down by "the west" although admittedly there was no way that "the west" was going to come to their aid in the way some of them wanted.
From what I can ascertain, the government has identified and backed a main arm of the rebellion and has chosen to support it with diplomatic support and now, hopefully very limited, military aid.
Backing (or at least not working against) Assad, a known war criminal from his earlier actions, was always going to be a sensible option until as I said earlier, he over-reacted appallingly to the initial peaceful (well-documented) protests and insurrection by basically bombing the bejasus out of civilians (no one seriously disputes that) and, critcially, unleashing a tide of sectarian bitterness that has threatened to have the conflict spill over into neighbouring countries.
Wiser people than me have concluded that this is a state of affairs that it would actually be in our interests to restrict as far as possible. The only people arguing against it seem either to be people who support Assad for whatever reason and refuse to believe in his crimes or those who, perhaps because of Iraq and Afghanistan, think that at the very mention of "foreign involvement" we are about to repeat past mistakes. An understandable view perhaps but maybe a short-sighted one. I certainly don't want to see the UK beconig embroiled in this conflict but I believe there are things we can do to help without that happening, and we should do them.