I don't feel the same way, to be honest. Though I understand the sentiment and the shared sentiment expressed earlier by Curious Cat in regards to seeing dismembered fetus parts.
If you define a fetus as being human solely on its potential to be a full fledged human one day, then by that logic, I would have the moral responsibility to go get knocked up whenever possible as my eggs also represent the potential for human life. But the majority of people don't expect this. Some do. Not most of us though (at least, not in North America).
Having the potential to be human does not actually constitute what we would call being human, and on the same vein, observing the potential for something does not morally inform you as to whether or not you ought to follow through with that potential.
Originally Posted by Agota
In my case, the reason why I'd consider fetus as a person of some form is it's potential to become a human being. I couldn't have an abortion, because I'd imagine the time when that fetus would actually become a child, a teenager, an adult and therefore I'd feel like I'm giving up on that, not on couple of cells combined together. Again, this is a personal opinion and it's wrong to try to force it on others, especially ones who might be in less favorable circumstances than you are. The fact that fetus has a potential to become a human being doesn't mean that anyone has a right to explain someone what they should or shouldn't do with their bodies.