I keep hearing that some Catholics support abortion as a matter of conscience. I'm not sure what they mean by this.

Apparently, this means some Catholics feel it wouldn't be moral for them to support the Church's teaching on abortion or that their failure to live by the Church's teaching doesn't bother their consciences. Of course, this says nothing about the correctness of the Church's teaching. It tells us only what certain Catholics think about things or, at least, what they say they think about things.

It's hard to understand how a Catholic couldn't in good conscience follow the consistent moral teaching of the Church and remain a Catholic, given that he is obliged to form his conscience according to that teaching.

This doesn't mean following Christian teaching is easy. No one said Christian moral maxims such as "love your enemies" or "do not commit adultery" are effortless to observe. The temptation to set down our own ground rules about what's right and wrong and expect God, the Bible, and the Church to change accordingly can be great. The Church will never alter its preaching to justify our practice.