I applied for my first conference and got rejected :-(. The reviewers had no remarks so I don't know why. I'm quite disillusioned, since I have the feeling I haven't achieved anything yet since I started in september last year, and all the people around me seem to got accepted for this conference (it is quite a large one). I really feel like a failure now...

Its depressing I agree but rejection isn't necessarily a reflection of the quality of the abstract you put in. The conference organisers have to put together coherent themes for all the conference sessions and it may just be that the paper you proposed was fine but didn't fit into any of the chosen themes. You shouldn't feel like a failure on this account.

On a more practical level, did your supervisor read the abstract and offer any feedback and once the conference programme is published can you see what the structure of the selected abstracts is to see if yours can be changed stylewise for future submissions?

Don't envy people around you whose abstracts were accepted.
Some presentations could have limited number of attendees or the presenters were criticised to have serious flaws in reasoning...
However, even some research scientists with PhD could get rejections for conference presentations.

However, you only started in last september!? This is too fast!

Thanks for your answers! In my department, almost everyone sent in an abstract, and most people started even later than me... But they all got accepted. My supervisor read the abstract and corrected it a little bit, but he really isn't that much of a support, I hardly see him because he has so many PhD Students.
But lately, I have the general feeling that all people around me know so much more and see their supervisors more often than me. But yeah, maybe it is just too fast...

Echoing the comments above, rejection can reflect simply the fact that your topic didn't mesh with the other submissions. There is also an art to writing an abstract, which you will pick up - have a look at abstracts that were accepted. At the end of the day, all academics have suffered rejections.

Try not to take it to heart - as others have said, it might be more to do with your research not fitting well with the sessions they had in mind. And yes, it's pretty early for you to be submitting conference proposals, especially for big events. My first big conference wasn't until halfway through my second year.

If you want conference experience, I'd suggest going for postgraduate conferences as it'll be much easier to get accepted. Also, try not to compare yourself to others quite as much. I bet most of the people around you who went for this event weren't also in the first few months of their PhD!