1. What does it mean?
Short for 억지로 까다, meaning to criticize or put something down unreasonably. A speaker may use 억까 when criticism of a person, post, or performance seems unfair or contrived.
2. The nuance
This labels the criticism from the speaker's point of view; it is not proof that the criticism is wrong. Friends may also use it dramatically over minor teasing.
3. Examples
“한 번 실수했다고 준비 안 했다고 하는 건 억까야.”
Saying I didn't prepare because of one mistake is unfair nitpicking.
“이번 사진까지 별로라고 하면 좀 억까 아니야?”
If you're calling even this photo bad, aren't you just looking for faults?
Sources
Korean Institute for Healthy Family: communication teaching resource
References support the meaning and usage. Example sentences are written for NoCapWiki.