I play "where did this word come from" games. Points are awarded for the most original origin. No points for the real etymology. Today's word: 'misled'
This word is made of 2 morphemes:
mi- and sled
As you can see it has the root word "sled" in it.
This comes from a misinterpretation of "me sled" in Middle English. People often will lax their vowels making "me sled" sound like "mi sled." People will often run words together for ease of articulation. Leading to the written form becoming "misled" instead of the original "me sled"
So now you know. "misled" is a variant of "my sled."
But, you might ask. What about the meaning of "to lead astray"? Think about it. If someone is on YOUR sled, and you wanted it back so you start pulling on it. It's easy to lead them down a path other than the one they wanted. All the while yelling, "mi sled! mi sled!" Consequently, we've now adopted it to mean "lead astray" and inserted the newer form "my sled" as the standard for possession.
And that is how it works.