That bit of illogic escapes me. No one, other than Trump and his team of yes-men, claim that.
Your words drip with political hypocrisy. Apparently, it was OK during the 1990s for Republicans to investigate and disable Clinton's presidency. Although the GOP-led Congress impeached him, the Senate voted against ratifying it – keeping Clinton in office. The radical Republicans who were behind that failed effort, claimed it was their goal all along to politically disable his administration. Now two decades later, it isn't OK for Dems to investigate a 'Republican' (and I use that term loosely) president.
My words above might be interpreted as implying that the accusations the GOP aimed at Clinton and the accusations the Dems aim at Trump are equivalent. They aren't. After more than 5 years of open-ended investigations, the Independent Council Ken Starr came up without any actionable findings. As Independent Council, a position no longer supported by law, Starr had more powers of indictment than did Mueller.
With his investigation of Clinton's possible adultery, Ken Starr was criticized of crossing a line – acting more as a political hit man than as a prosecutor. Now you claim that Mueller's investigation was an effort to "destabilize" Trump's administration. How can you not see the hypocrisy in that?
Besides, Trump's words and actions destabilized his own administration. That ship sailed a long time before Mueller or James Comey were house-hold words.