Employers are usually looking to find whichever candidate they feel best suits their needs; it is reasonably common for interviewers to be flexible with their dates up to a point.
If they have already offered you the interview, then that means they're already interested in meeting you; asking for flexibility with the dates doesn't affect your potential suitability as a candidate. Of course, they may also have some perfectly valid reasons to decline as well.
If the employer is interviewing other candidates who they might realistically expect to make an offer to, then they will be aware that the "best" candidates might also take other job offers. Of course this isn't a problem if you are able to get an earlier interview, but if you get a later interview then you may put yourself at a disadvantage.
They might already be at the end of a very long interview period, in which case they may be committed to a decision date for all their other candidates.
They may have some other internal reason which prevents them being flexible -
e.g. maybe the interviewer(s) are only available within a very narrow window of opportunity (remember they might have holidays or other commitments too.)
If they ask the reason, be honest. Having a pre-booked holiday is irrelevant as far as your suitability for the job is concerned. On the other hand, being cagey and/or secretive over something that they will perceive as a rather trivial matter simply looks unprofessional.
Remember that you are the one asking for flexibility from them; you don't need to immediately offer to interrupt your holiday. If you really do want the job however, you are going to need to decide whether you are willing to interrupt your holiday just in case they decline.
If they decline to be flexible and you are willing to interrupt your holiday then stay professional and don't make a big deal of it - you do not need to rattle out a long story about all the details of how disruptive it will be or how long it will take you to travel. Simply tell them that you understand they're not able to change the dates and this isn't a problem; you will be attending the interview at the previously arranged time, and you look forward to meeting them. That's all you really need to say in the conversation; anything extra is unnecessary (unless they ask out of politeness or curiousity of course).
If they do ask how disruptive it will be to your holiday; again, be honest but also don't dramatise it or make a big deal out of it. Your mindset at this point should be that you've already decided that you are really keen on the job and you are perfectly OK with the interruption.