What they thought is irrelevant in a country that believes in the rule of law: they were attacking the highest institution of one branch of government with the express purpose of forcing them to overturn the legal result of the election and install their preferred president. This is an (attempted) insurrection, and there are no two ways around it.
Comparing this to an attack on a courthouse is patently absurd. Especially since the courthouse was not attacked for 'toppling the government' - I can't even imagine where you came up with that - but because it was known that arrested/kidnapped protesters had been held inside the courthouse building. In general, none of the BLM or Antifa protesters are interested in "toppling the government" - they are interested in "toppling" the police and in stopping the white nationalist fascists that police are openly supporting from taking over the country.
Yes, I called it insurrection earlier. You've replied to my comment out of context of the reply which preceded it, so your strawman of me doesn't make any sense.
>they are interested in "toppling" the police and in stopping the white nationalist fascists that police are openly supporting
I wrote a longer reply to your comment, but then I deleted it. DC metro police are more than 50% black, it's a joke that they would "openly support white supremacists."
The Portland courthouse siege- OP's chosen example- was led by violent white anarchists. Their motive was to topple the government. Portland's Black Lives Matter activists complained many times that their cause and movement had been hijacked [0][1][2].
The people who invaded the capitol today, at least some, probably thought they were protecting democracy. They may have thought they were defending election integrity. They were wrong. That doesn't mean they are evil or amoral. It means they are misinformed and misled. Using them as a foil to downplay other, much more violent unrest is neither helpful nor informative.
I haven't seen photos of armed rioters in the capitol. If you have some, please link them.
[0] https://www.kgw.com/article/news/local/professor-focus-of-po...
[1] https://komonews.com/news/local/black-people-in-portland-str...
[2] https://www.latimes.com/opinion/story/2020-09-04/black-lives...