I know this is just a big religious bashing thread but here's a serious answer (and no, I'm not catholic):
The reason meat was picked as the thing to abstain from is that in prior decades and centuries, meat (as opposed to fish) was a special sign of feasting and rejoicing since it couldn't be had every day. Thus it was appropriate to deny oneself this sign of rejoicing as a gesture of sorrow for having offended God by one's sins. However, fish (as opposed to meat) did not have this connotation. Fish was not a special sign of rejoicing the same way that meat was, as it was less expensive and did not require slaughtering one of the animals of the flock or herd.
A second reason, which is perhaps more relevant (but in my opinion a little less biblically based) to those of us in the developed world today, for whom meat and fish are both equally available (and for whom fish may be even more expensive in the supermarket) is that fish is a symbol of Christ and by eating fish on Friday we are symbolically nourished by Christ while denying ourselves other forms of animal sustenance.
edit: Main point is that you deny yourself something that you really enjoy as a gesture of sorrow and repentance for sinning.
The reason meat was picked as the thing to abstain from is that in prior decades and centuries, meat (as opposed to fish) was a special sign of feasting and rejoicing since it couldn't be had every day. Thus it was appropriate to deny oneself this sign of rejoicing as a gesture of sorrow for having offended God by one's sins. However, fish (as opposed to meat) did not have this connotation. Fish was not a special sign of rejoicing the same way that meat was, as it was less expensive and did not require slaughtering one of the animals of the flock or herd.
A second reason, which is perhaps more relevant (but in my opinion a little less biblically based) to those of us in the developed world today, for whom meat and fish are both equally available (and for whom fish may be even more expensive in the supermarket) is that fish is a symbol of Christ and by eating fish on Friday we are symbolically nourished by Christ while denying ourselves other forms of animal sustenance.
edit: Main point is that you deny yourself something that you really enjoy as a gesture of sorrow and repentance for sinning.