What is monogamy supposed to mean for me?

I apologize if this isn't the right subreddit, but I just don't know where else to go. I sincerely fear being judged for what I am about to say as it is though.

I want a monogamous relationship, but am constantly eyeing and getting to know other people that I see relationship potential with. As in, I would like to date these people, love on them, pursue something. At the same time, I want to have someone that is devoted to me.

Look, I understand that's completely selfish. Over my 28 years I have learned this the hard way. But I honestly am unable to fathom being dedicated to one person completely, ever. Sometimes I feel as though I want to be dedicated to just one person...when I'm close to losing my girlfriend over another girl. But once I feel secure in that relationship I begin wondering again. I'm very personable. All sorts of people like me. Why can't I like all sorts of people?

I doubt it's a developmental issue. That is, I don't know if I can just grow out of it...grow into someone "more mature," "less selfish," etc. But maybe I can. If not, how do I deal with these feelings? What if I just simply cannot be monogamous?

Ugh. Is there something wrong with me? Society? The concept of love itself?