Someone mentioned the Final Fantasy VII bit, but there's a bit more to it than that. If you really care about SPOILERS for a game that was released 13 years ago, don't read the rest of this.
First, Tifa does start off weaker than Cloud; he begins the game at level 5 and likely gains a few levels before you get to play as her, and she starts at something like level 4. She's pretty much where you would expect someone to be as a gifted martial artist but otherwise normal human being. That applies to Aerith as well, who you get even later and who starts at the same level.
On top of that, Cloud never was a member of Soldier; he was just one of those blue-suited grunts you were dropping like flies during the opening scene. He didn't have the strength or charisma you'd need to join Soldier, much less become a high-ranking member. He did have some military training, but he was still just an ordinary guy. The big thing that bumps him up over the rest of the party was the whole Mako exposure/Jenova cell injection he got before the events of the game, which you could use to explain his bump up from level 1 (as a grunt sent to Nibelheim) to level 5 (as he is when the game starts).
Of course, you could also say the whole thing is an arbitrary power limiting system set in place to even out the gameplay, and doesn't necessarily mean anything as far as the storyline is concerned. It's ridiculous, but it's also probably the most likely explanation.