Are the parallel elements in a matroid just behaving like loops? If so, why?
For example, in $U_{2,3}$ if we contract an element what will happen? In $U_{2,2}$ if we contract an element what Will happen? In $U_{2,5},$ if we contract an element what will happen?
An element $e$ in matroid is a loop if $r(e) = 0$ (this is a definition). Two non-loop elements $e, f$ in a matroid are set to be parallel if $r(\{e, f\})=1$. The unifying concept here is that both loops and a parallel pair are circuits, i.e., minimal dependent sets. In other words, they are both sets of cardinality one more than their rank. If you are familiar with graphs, the above translates to loops are loops in the graph sense, parallel elements are parallel edges, and both are cycles.
In general, for the uniform matroid $U_{m,n}$ and a set $T$ of $t$ elements,
$$U_{m, n} / T \cong \begin{cases}U_{0, n-t}, & \text { if } m \leq t \leq n \\ U_{m-t, n-t}, & \text { if } t<m .\end{cases}$$
So contracting an element in $U_{2,3}$ yields $U_{1,2}$, contracting an element of $U_{2,2}$ yields $U_{1,1}$, and contracting an element of $U_{2, 5}$ yields $U_{1,4}$. This can also be seen by the definition of contraction, or pictorially, where contraction can be interpreted as a form of projection operation, as outlined in James Oxley's Matroid Theory book, chapter 3.