avoidant relationships?

Because it is non-scientific terminology, it basically means whatever people want it to mean when they speak or read "avoidant". 

For example, the following are all different, "avoidants of ..." 

A: getting hurt ( all biological life )

B: certain cultural marks ( cultural life )

C: verbalising emotions ( some are just incompetent )

D: empathy without incentive ( economically rational/ calculative )

E: explicit commitment ( economics again, but more formal )

-- and that's just a few