Why do we always wake up at the climax of our dreams, even when it is an alarm that wakes us? I know that it probably has something to do with the fact that our dreams didn't really end at the same time our alarm clock rang, our brains just make us think so for some reason.
There are two possibilities. One is that we do tend to wake up more at the climax of dreams, and that somehow our dreams can sync up with external input like an alarm clock so that the climax of the dream occurs at the same time as the alarm going off. The second is that this doesn't actually happen; the alarm is just as likely to go off at the climax of the dream as it is at any other point.

If the second situation is true, then why do you end up feeling like you always wake up at the climax of the dream? One explanation is confirmation bias. This is an established bias of human memory, in which we selectively remember events that confirm our ideas, and neglect the events that disconfirm them. In this situation, you have the idea that you always wake up at the climax of dreams, so your memory is biased towards times where you actually did wake up at the climax of dreams. However, there are likely many times where you woke up not during the climax of the dream, but these are less memorable because they don't fit your expected pattern.