The basic advantage of a carrier over other capital ships is that it deploys relatively cheap, expendable, effective, and rapidly responsive craft to seek out and attack or intercept threats while they're too far out to harm the capital ship. That type of deployment sounds like it might be a really good idea in a space battle, just as it is in naval warfare today.
Yes, but that's where you use missiles instead of fighters. That's where the horizon issue comes into play. At least in the days before satellite communication, carriers needed to send human-piloted fighters rather than missiles because there was a limit to how far they could see and therefore target an enemy. It's a solution that developed in response to the conditions on Earth
. It's lazy to just want to transpose that exactly to space.
Look, I'm not interested in debating this whole thing yet again. Military talk bores and depresses me. I'll just refer you to where I got the ideas from, a site that demolishes the space-fighter idea more thoroughly than I could:
Debate it with them if you like.