To argue.

Friendship, as many other kinds of relationships, is not all about rainbows and sunshines. There are also times when a partner had a different perspective with the others, leading them into an argument or a fight.

Allen and Lenalee had their first fight not long after they started getting to know each other. It happened during their mission in the Rewinding town. When they were fighting the akumas, Road ordered one of the Akumas to self-destruct in 10 seconds. Road said that the Akuma's soul won't be saved unless an exorcist uses Innocence upon it. Allen panicked. He desperately tried to exorcise it before it exploded. Lenalee stopped Allen and protected him before he reached the Akuma.

As Allen watched the akuma's soul disappeared in vain, he became very enraged and yelled at Lenalee for stopping him. Lenalee, on the other hand, was not amused of his attitude, and slapped him.

Allen: "Shit—why did you stop me?!"
Lenalee: "Because we're friends!"

Allen's reaction might look excessive, but I think he was simply following his intuition. What makes Allen different with any other exorcists? Look, one of the reasons Allen decided to become an exorcist was for the sake of Akuma. He exorcises them not just to "destroy" them—instead, it is to "save" their souls. Thus, without giving it a second thought, he just tried to reach the akuma and exorcise it before it exploded—but he wasn't alone; Lenalee was there. She probably didn't know much about Allen's past yet and what it had to do with his reason for being an exorcist. However, that time she had her mind a little cooler than enraged Allen, she foresaw that Allen's attempt to "save" the akuma wouldn't be successful and that the explosion would endanger his life instead.

Lenalee treasured Allen as her companion, and she wouldn't want to see her companion dying in front of her, that's why she decided to stop him—her effort risked her life as well—it was all to save him. I don't think I can blame either of them. They hadn't known each other very much back then. They hadn't learned the other's background and perspective—so they clashed. But yes, I agree that Allen should give more credit to himself.