Alright, this is what I've always thought:

First of all, he wouldn't have been going to the Fire Cavern when he got into his brawl with Seifer because like so many people have said before, you need "support" for that place, and from the FMV, I think it's accepted that he was alone.

Second, I believe that he and Seifer were truly practicing and Seifer just took it too far. I think that Squall wanted a warm up with someone who would give him a good fight before he went to the Fire Cavern. I don't think they were such bad enemies that they didn't practice together.

Obviously this all took place outside nearby mountains somewhere close by Balamb Garden.