The reason for this is that the letter "i" in "climb" is followed by a consonant ("m"). In general, when the letter "i" is followed by a consonant in a single syllable word, it produces a short vowel sound.
Here are some other words with a short "i" sound:
* ship
* fish
* trip
* spin
It's easy to get confused because we often think of words like "time" and "bike" as having long "i" sounds. However, these words actually have a diphthong - a combination of two vowel sounds - instead of a long "i".
So, remember, "climb" has a short I sound, just like "sit" or "pin".