Critically means in a way that judges severely, or dangerously so. Critically ill, critically acclaimed, look at it critically.
The two senses are far apart: critically ill means at risk of dying, and critically acclaimed means the critics liked it. Thinking critically means examining an argument rather than attacking it.
1adverbcriticallyIn a way that judges severely, or dangerously so.
“The report spoke critically of the hospital's poor record on hygiene.”
critically is a manner.
From critical + -ly.
Etymology from Wiktionary, CC BY-SA