The spelling of the word "in spect" can be explained using IPA phonetic transcription. The first syllable "in" is pronounced as "ɪn" which is the short-i sound. The second syllable "spect" is pronounced as "spɛkt" which follows the traditional spelling rules. However, the pronunciation of "spect" also follows the Latin origin of the word "spectare" meaning to look at or observe. So, even though the spelling may seem odd, it is a result of the word's etymology.
The word "inspect" comes from the Latin roots "in-" meaning "in" or "into" and "spicere" meaning "to look" or "to see". The prefix "in-" denotes a sense of going into or looking closely at something, while "spicere" refers to the act of seeing or observing. These Latin roots eventually evolved into the Old French word "especier", which meant "to observe". Over time, the "e" was dropped and the word became "inspect" in English, maintaining its meaning of examining or scrutinizing with attentiveness.