It sounds to me like your boyfriend either has a very low tolerance for frustration or he lets frustration build up to the point that the slightest little thing makes it all spill out at once. He doesn’t have anger issues so much as insufficient coping skills. To his credit, he doesn’t take his frustration out on the people around him, only at objects. That means that he does have some control. People with genuine anger issues usually don’t. But he is controlling his feelings rather than dealing with them.
A therapist only has what the client presents to work with. My guess is that the therapist was correct in assessing your boyfriend as not having issues with anger. What the therapist didn’t understand was how anxious your boyfriend gets when things don’t go his way.
If your boyfriend will accept your help, you could go with him to a therapy appointment and explain what you see. Your boyfriend could use some help learning new and more effective ways to cope with mistakes, with unexpected disappointments, and with a buildup of pressures. Life without adequate coping skills is hard on the person and hard on the people around him. You both deserve better.
I wish you both well.