Actually, Ash (as explained in the earlier stages of the series) is in deed very, very stubbron!
Many times he pushes his pokemon on to their very limits ignoring the situation. such as the gym battle with Brawly, Lt. Surge, Viridian city, and Bliane. All four were battles in maintaining his pride in his pokemon as well as the one with Lorelei.

Some of them he made new limits for his pokemon, other times he got them hurt. So it's all because of one thing :
Ash is more headstrong than brainsmart (period).