This is a cornerstone of Predator personality though. Even Wolf, the supposed professional cleaner, could not help himself but to strip off his gear and wag his schlong around at the Predalien. It's who they are.
In fact it's that duality of the two species that makes them work so well together. The Predator is ultra alpha, ultra confident, incredibly strong, armed to the teeth, and prone to ego. The Alien is unrelenting, unstopping, unwavering, cunning, and resilient.