Here's why:
* Stress: The stress in "transmit" falls on the first syllable ("trans").
* Short vowels: When a vowel is followed by a single consonant, it's usually a short vowel sound. In "transmit", the "i" in the first syllable is followed by a single consonant ("t").
So, the "i" in "transmit" has a short "i" sound, similar to the "i" in "bit" or "sit."