Partial orders are formalized by weak inequalities $\geq$ rather than strict ones $>$. We then add an additional axiom which says that $x\geq y\land y\geq x$ implies $x=y$.
But it seems to me that we can instead speak of strict inequalities, and replace that axiom with the axiom that $x>y\implies \neg y>x$, and that $\neg x>x$.
I am not claiming that this is “better”, just that it seems a bit more intuitive to me at first glance. Why has it been chosen to formalize orders according to weak inequalities, rather than strict ones?
The reason is that there is the related notion of a preorder, which is a reflexive and transitive binary relation. An antisymmetric preorder is a partial order. Furthermore, if $\leqslant$ is a preorder on $X$, then the relation $\sim$ defined by $$ a \sim b \iff a \leqslant b\text{ and } b \leqslant a $$ is an equivalence relation, and the preorder $\leqslant$ induces a partial order on the set $X/{\sim}$. This construction often occurs in mathematics.
As one cannot use $<$ to define a preorder, the notation $\leqslant$ is preferred, even for an order.