Because someone has to. For the word “instinct,” from Latin instinctus “instigation, impulse, inspiration,” noun use of past participle of instinguere.

• in - "into, in, on, upon"
• stinguere - “prick, goad,” from PIE *steig- “to prick, stick, pierce”

So, in the end, the “stinct” has more to do with the word stick than it does stink.

Here’s a reference link. www.etymonline.com/word/instinct