https://www.buzzfeed.com/katieherzog/how-i-smoked-my-way-sob...
The idea that cannabis can cause liver damage seems to have started from a study[1] on the effects of chronic marijuana use in patients with Hepatits C, a disease which primarily affects the liver. There was a correlation between heavier cannabis use and worse liver fibrosis, but I think it's pretty misleading to say "cannabis can damage the liver" - so can acetaminophen, vitamins, and a million other chemicals, if taken in vast excess or with an already compromised liver.
[1]http://www.cghjournal.org/article/S1542-3565(07)01050-6/abst...
I'm not sure how you can say that with any degree of confidence though. The study you reference refers to cannabis use in people infected with hepatitis C. Have you seen any results comparing the effects of alcohol on the liver in a similar cohort of patients?
The reason I believe it is admittedly anecdotal, but I still find it compelling: I've simply never heard of someone experiencing liver failure from chronic heavy cannabis use alone, whereas chronic heavy alcohol use alone is known to practically guarantee liver failure.
See my sib comment. In short: it's a misinterpretation/decontextualization of the research.