Let $C$ be a model category, $B$ an object. We take the coproduct of $B$, $(B\amalg B,i_0,i_1), i_0:B\rightarrow B\amalg B, i_1:B\rightarrow B\amalg B$ injections and then factor $(Id_B,Id_B):B\amalg B\rightarrow B$ as $(Id_B,Id_B)=s\circ f$ where $Id_B:B\rightarrow B$ is the identity map, $f:B\amalg B\rightarrow B'$ is a cofibration and $s:B'\rightarrow B$ is a trivial fibration.
Then since $Id_B$ is an isomorphism, it is a weak equivalence. And since $s$ is also a weak equivalence(trivial fibration), by the 2 out of 3 axiom, $i_0\circ f,i_1\circ f$ are weak equivalences.
I was wondering if $i_0,i_1$ are also weak equivalences.
No, certainly not. For instance, if $C$ is the category of topological spaces with its usual model structure, $B\amalg B$ is a disjoint union of two copies of $B$ and $i_0$ and $i_1$ are the inclusion maps of the two copies. These are not weak homotopy equivalences unless $B$ is empty, since they are not surjective on $\pi_0$ (since each copy of $B$ is clopen in $B\amalg B$).