Definition of Reflexivity (Wikipedia):
In mathematics, a binary relation R over a set X is reflexive if it relates every element of X to itself. ∀x ∈ X : x R x
It can reflexive since it could be $a=b$ ($a,b\in\mathbb{R}$) But it could also be irreflexive: Since it doesn't have to be equal.
Should I think like this: $a\leq b$ is reflexive since we got the relation $\leq$, which implies it doesn't have to be equal but until we don't know the results it's reflexive.
Kinda not the smartest question, but I'm fairly interested into the thought process of yours :)
*pardon for my bad English, I'll look to improve it further.
A relation $R$ on $A$ is reflexive if $(a,a)\in R$ for all $a\in A$.
In particular, the relation $aRb$ iff $a\leq b$ (either $a<b$ or $a=b$) on an totally ordered set $(A,<)$ is reflexive since $a\leq a$ for all $a\in A$.