Why do very different people attract each other? I have noticed than many couples are very different from each other but yet they fell in love in spite their differences. I was wondering about the psychology behind this. 
Why would someone want to be with someone that has different likes
Concepts like love and attraction are not only poorly defined, but in this context are too complex to discuss meaningfully, if a scientific answer is what you are after. It is also hard to quantify 'different' when it comes to people - there are just too many variables to compare.

But, there is actually some principles and models that could be part of a more complete answer.

Total Free Energy

Both the TOTAL1 model (an extension of the famous TOTE2 model), or the free energy principle3, assert the following:


  Us humans constantly form predictions that serve as expected state, and then compare them to the actual state of the world/body (via senses).


This applies to both micro levels (say, communication between neuron layers) and micro level (consciousness).

It then goes:


  When the predicted state matches the actual state, nothing to do. When there is incongruity, we must either change our predications (models/goals) or the world (by acting).


In this view, the brain is largely a differential processor - rather than processing stimuli all the way bottom-up, it generates top-down predictions and only left with validating them against stimuli.

This is a hugely efficient optimisation strategy for the sake of metabolic economy.

It also goes to explain:


Why we stop perceiving mechanical clocks after spending some time in a room.
Why new objects (shoes, houses) excite when new but hence after peter out.
Why relationships tend to cool-off over time (and in turn why some people cheat on their partner).


In extremely general terms - that that doesn't change doesn't excite.

Now back to Friston:


  For survival sake, all living things strive to minimise surprises by forming and updating a model of their environment.


Things get interesting when survival is no longer a concern...

Diversity

Taking into account the said above, picking someone who's different from you in many aspects means your mental models are challenged more often, which could yield excitement.

I think a good example is dating someone of different nationality, say a Westerner dating an Easterner. Differences can go both way (good and bad), but it is exciting nevertheless.



1 Wang, C. and Mukhopadhyay, A., 2012. The Dynamics of Goal Revision: A Cybernetic Multiperiod Test- Operate-Test-Adjust-Loop (TOTAL) Model of Self-Regulation. Journal of Consumer Research, 38(5), pp. 815-832.

2 Miller, G.A., Galanter, E. and Pribram, K.H., 1986. Plans and the Structure of Behavior. Adams Bannister Cox.

3 Friston, K., 2010. The free-energy principle: a unified brain theory?. Nature reviews neuroscience, 11(2), p.127.