Fear of Babies

I have a certain feeling towards babies of other people. I feel more or less uncomfortable being around other people's babies. By babies I mean young children who are not able to eat, walk, or talk on their own, up until about two years of age. This feeling is something that has come about just in the last few years, when there have been a lot of new babies who have been introduced to me, who I am not directly related to.
Not being directly related to a baby puts a person in a situation that could make him or her a little uneasy, like me. In recent years, I have had older cousins and relatives of close friends who have had children. And in family gatherings and such, I have been placed alongside the rest of my family with close contact with these newborns.
What makes me uncomfortable first of all, is the fact that I don't really know the cousins or relatives themselves very well, much less, their newborn children, and I don't exactly feel right about holding the babies or giving affection to them, for the main reason that I don't really feel any affection towards them to begin with. When being introduced to a baby, there is really not any kind of guideline or code of etiquette to employ. Any kind of greeting, from a tiny handshake to a showering of kisses to a monologue of incomprehensible nonsense words will do. The baby doesn't really feel anything. He/she has no idea who you are, and probably doesn't care either.
Therefore, the only goal to keep in mind when being introduced to a baby is keeping the parent(s) in mind and not embarrassing yourself or making them feel weird about letting you be around their baby. I have been in close contact with babies since I was very young. Being the oldest of four children, I witnessed the births and upbringing of my two youngest siblings, and was thoroughly involved in their immediate childhoods.
I did a lot of holding, nurturing, caring for, and giving affection to my little brothers, and have remained an important part of their lives since then. I feel that by being introduced to someone at a young age helps to grow an attachment to that person, and I feel very attached to all of my siblings. On the other hand, that kind of attachment is not something I would try to develop with any of my cousins' kids or any baby that I am not going to be around for the majority of his/her upbringing. Thus, I would just as soon not be introduced to any of these babies at all, and just kind of observe them from a distance, rather than be placed in the limelight and responsibility of showering them with attention and holding them.
I have another fear of holding babies that stems from my childhood when I dropped my older younger brother, Ethan, when he was only a few months old, breaking his leg. I don't think I have ever fully recovered from this, even though he recovered just fine, and doesn't even remember it. I do not like holding babies as a result of this, and I feel especially uncomfortable holding a baby who is not mine or closely related to me. I have tried and will continue to try avoiding this responsibility until it is time for me to hold my own children and I can actually cling to them.
I don't think my "fear" of babies is exactly irrational, and I don't think it's exactly a fear at all, but I coined it that way because of the way it makes me feel. I would just as soon get to know these children from the age when they can actually remember me and have fun with me, rather than just stare and bubble at the mouth. Until I have my own spitting image staring and gurgling back at me, I will wait to get intimately close to a baby.