The Alpha-Beta female seeking Alph-Beta male

So the other day, I was having a wonderful conversation with one of my Alpha Female friends. Among the topics, were boys and men and how we interact with them. She has long since told me, that I act very much like a dude in a relationship, but I still have the essence of a lady.
This was not news to me, I already had this self discovery. But what she said next surprised me, she said, "Andrea, you need a Beta male". I looked at her like she had lost her mind. The mere idea of dating a man, that would oblige my every whim is extremely unattractive. I do not want to have the ability to bark jump, and he looks at me eagerly waiting to say how high, how many times, and which directions. So I stated, I probably would best fit with an Alpha male. Someone who is opinionated, mentally strong, driven, and willing to ATTEMPT to put me in my place. I want the challenge, the devil advocacy, you know the fire. I'm not saying I want a relationship full of debates and trying to be one up, but I am saying that I want someone who has a backbone.
Then my dear friend brought up a good point. An Alpha Male will always want to be in charge, and might not see you as an equal. I already know how stubborn I can be, and If I do not see the other person making an attempt to compromise, then I am standing my ground. I'm also to feisty to have someone dictate to me, and think I will hop to do it. He may think its cute at first, like awww she's trying to be difficult. After a while he may just get irritated with my inability to comply to his request.
When the conversation finally concluded, I believe the best person for me would be an Alpha-Beta male. I most certainly belive that I am an Alpha-Beta female. Yes I may have my demands, I can take charge, lead, and walk around like I own the place, have my opinions (and willing to express them), have a low tolerance for bull, and what not. But I can also compromise and meet someone half way, I prefer to stand side by side, believing no one should really be leading the other. I want this sense of equality in my relationships.
As I assessed some of my past ones, I've dated quiet of few Beta males, who perpetrated being Alpha males. The truth would eventually come out. I dated two Alpha males,one was a bit too much on the jealous side. Basically, I felt like a lot of my past relationships did not have a balance. Considering how stable I like to be, those rocky relationship weren't cutting. I know there will never be a perfect relationship. I am not looking for perfect. I just want to know my man is just a strong minded as I am, but will to meet me half way when the time calls for it.

What do you think?