Total Order Relation Given $X = \{ a , b , c \}$ and $R = \{ (a,a) , (b,b) , (c,c) , (a,b) , (a,c)\}$

Is $R$ a total order on $X$? 

I know that total order requires the relation to be comparable on all elements, anti-symmetric, and transitive.

What I am confused about is that I was told this relation is NOT total order, but I do not see how the elements cannot be compared, because they surely are anti-symmetric and transitive. 

Can't $a$ be compared to itself? Surely $(a,b)$ and $(a,c)$ pass the comparability test, so all that remains must be the reflexive examples. 

Clarification is greatly appreciated, thank you for your time, patience and assistance!
A total order relation requires 4 things:
1)refxivity(it is reflexive in this case)
2)anti-symmetricity(it is anti-symmetric) 
3)transitivity(it is transitive)
4)comparibility
Now compatibility means that if you choose any two elements say a,b then either aRb or bRa
But in this case if we take for example b and c, neither bRc nor cRb so the relation is not compatible and hence is not a total order.
Is this relation transitive?. I don't think so.
We have (a,b) and (a,c). 
To be transitive, (b,c) must be a part of relation too. 
So, this is not a total order relation because is not transitive.