I don't reach out to initiate friendships with new people because I feel sure they don't want to be bothered. Even with established friends, I won't ask to hangout unless I have an event that I can invite them to so I won't waste their time.
When people say they'd like to hang out, unless they reach out with a specific invite, I assume they're just being friendly.
A family member thinks I'm wrong on how I'm looking at all this. How would I know?