Let $B$ be either $B_{\text{dR}}$ or $B_{\text{crys}}$. For a $\mathbb{Q}_p$-representation $V$ of the absolute Galois group $\mathrm{Gal}(\overline{K}/K)$ of a $p$-adic field $K$ (a finite extension of $\mathbb{Q}_p$), there are subspaces of $H^1(K,V)$ defined by $\ker(H^1(K,V)\to H^1(K,B_\bullet\otimes V))$ for $\bullet\in\{\text{dR},\text{crys}\}$. Each element of the subspaces of $H^1(K,V)$ correponds of an extension of $\mathbb{Q}_p$ by $V$ in the category of $\mathbb{Q}_p$-representations of $\mathrm{Gal}(\overline{K}/K)$ having some nice properties -- being de Rham/crystalline. The constructions of the rings $B$ seem quite complicated. My question is

How did we end up with the such complicated constructions of $B$'s so that elements of subspaces of $H^1$ having such representation-theoretic properties? Or, why do elements in $\ker(H^1(K,V)\to H^1(K,B\otimes V))$ have such representation theoretic properties?