–verb (used without object)
6. Informal. to get on well together; agree.
7. Obsolete. to prosper or succeed.
—Verb phrase
8. cotton to or on to, Informal.
a. to become fond of; begin to like.
b. to approve of; agree with: to cotton to a suggestion.
c. to come to a full understanding of; grasp: More and more firms are cottoning on to the advantages of using computers.
First time I've heard/read it in that context too so you're not alone. Learn something new every day. ..
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