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The Sith allow it, while the Jedi condemn love...
A loved one gives us strength.
The fear of losing a loved one is fear.
Fear leads to the dark side.
In my opinion, being closed off is correct – if you don't want there to be a POSSIBILITY of falling to the dark side. The Jedi are overly cautious, and this is further proof of that, but it is also the only way to protect the Force from bad influence.
Listening to Bastila, you can see this closed-off nature. And Obi-Wan, while remaining an exemplary Jedi, is a rather open person.