Getting from "other people's minds are probably similar to mine" to "I care about other people's minds" still requires some implicit premises or some psychological features beyond egoism (e.g. empathy).
Specifically it requires "I care about myself" with saner boundaries around what counts as 'self' as the implicit premise.
Added: Any specific reason for the downvote?
This is our monthly thread for collecting these little gems and pearls of wisdom, rationality-related quotes you've seen recently, or had stored in your quotesfile for ages, and which might be handy to link to in one of our discussions.