- It stinks
- It leaves soot and partially burned plastic on the wire and between the strands - those makes solder joints more difficult to make and less reliable.
- It is difficult to control how far back the insulation melts.
- Some insulation materials will soften and sag further back from the burned place, compromising the insulation.
- Lighters are hard on your fingertips if you use them a lot.
- Some wires have flame retarding chemicals in their insulation. That doesn't just stink, it can be poisonous.
- Teflon flu caused by breathing the fumes from overheated teflon. (Thanks to @JonRB - I had never heard of that before.)
Insulation is rarely made of rubber. It is usually some kind of plastic. There's also teflon insulated wire, which doesn't burn well but melts. Then there's what's called silicone insulated wire, which is especially heat resistant.
There's also varnish insulated wire meant for winding coils. Of all the wire types, you will most often see recommendations to burn the insulation off of varnish insulated wire. Don't.
For normal insulation, use a good tool.
For varnished wire, use (very) fine sand paper on the thicker wires. For the finer stuff, get a blob of hot, melted solder on the tip of your soldering iron and run the tip of the wire through the blob to melt the varnish off.
A good tool is expensive. I've never found one that I liked, that worked well, and that I could afford.
All the cheaper tools end up cutting into the wire. I've given up on ever finding a good, affordable tool.
I learned long ago to use side cutters to strip wire. I can do it without cutting or nicking the wire inside.
I also quite often use the smaller blade of my pocket knife. I keep it just barely sharper than dull. It can score the insulation, but not cut it well. Wire between thumb and knife blade, a half turn to score the insulation, then pull. Works like a charm, and doesn't cut or nick the wire.
I've already described magnet wire.
That leaves teflon insulated wire wrapping wire.
The wire inside is very thin, and any nick will make it break. Can't use any bladed tool on it because they will all nick the wire.
Just push the tip of the wire into contact with a hot soldering iron. I do mean just the tip - the wire almost always protrudes a tiny bit out of the insulation. Heat that tiny wire protrusion. It will get hot and the insulation will melt back maybe a millimeter or two. That's enough to solder with. Looks ugly, but it won't break off like it would if you used a bladed tool on it.
You don't want to use a sharp knife or a scalpel. You will be guaranteed to cut into the wire. (Or as RoyC mentions, your finger.)
Try it as I described. It works, though it takes some practice.