Why Was The Capitol Breached But Not The White House?

There are really only two explanations:  One is very tin-foil hat and the other disproves the media narrative.

First, the conspiracy explanation:  The Democrats wanted protesters to get into the Capitol as a way of taking the wind out of the very fishy election.  I think this is unlikely because, unhinged as they are, I do not (yet) think they are that evil.  But mostly, I don't think they have the physical bravery to take that sort of personal risk.

Second, while the media narrative is that leftist's protests are always peaceful or mostly peaceful, anything conservative is considered very threatening.  Remember the TEA party protests?  They were like geriatric garden parties but always described in the darkest terms.  What really happened is that everyone knows that conservative protests are peaceful.  So, when one turned out to be only mostly peaceful, the police presence was wholly inadequate.  

Contrast with protests outside the White House:  The mostly peaceful protests had left American cities shell-shocked, burned and boarded-up.  Of course the security outside the White House was tight.  It wasn't as if ANTIFA and BLM were Boy Scouts, security forces knew what they were facing and were prepared.