Jesus came to care for the "sick" and not the "doctors", but I'm sure some "doctors" were curious about what he was teaching...so Jesus spoke in riddles. Those with the Spirit (and maybe even the appropriate attitude) would understand the meaning behind the paradox. Those who didn't would scoff and walk away.
The relationship between the Fruit of The Spirit and the Beatitudes is the Holy Spirit, it seems like its more of a visual result of having the Holy Spirit. Others would be able to look at you and see if you if you are poor in spirit - or full of yourself. Meek (humbly patient or docile) or not. etc...AS WELL AS being able to see in others (and in oneself) the visual result of having the Holy Spirit by an increase in love for others...joy no matter what circumstances one is facing, etc...
Galatians 5:22-23 (New International Version)
New International Version (NIV) Copyright