This is a good question.
What are the various criteria for subjective attachment, and how are they weighted/prioritized?
I'll be very interested to hear others' answers.
For me, the deepest attachment is to pipes that my wife and children gave me as presents.
These are NOT my finest pipes, by objective standards. These are mostly inexpensive factory pipes. TBH, a couple of them don't smoke wonderfully. But these are infinitely more valuable to me than the finest artisan pipes I bought myself. If the house were burning and I had to save some pipes and not others, I'd save these gifts from wife and kids and let my finer pipes burn.
My second tier of emotional attachment is to pipes that my kids are particularly fond of and have expressed interest in inheriting someday. A couple of my kids have just really latched on to this or that pipe, in terms of their own aesthetic preferences. I'd prioritize keeping those around, for them.
A close third would be gifts from non family members. Friends.
Fourth tier would be my best smokers.
Fifth tier would be visual aesthetic preference.