People go on about this song "oh it's so beautiful", "oh it's so sincere". But I find it ugly and insincere. Which doesn't mean that I think people are wrong to like it, just that they've missed something.
Context is huge. John Lennon stated in interview that he was a wife beater, through jealousy. Read the bit in the wikipedia page on him about his relationship with Cynthia Lennon.
The Beatles song "Run For Your Life" on Rubber Soul (1965) is another song Lennon wrote (well, Paul McCartney gets co-writing credits) where a jealous guy threatens to murder his "little girl" if she does anything with another man. The line "I'd rather see you dead, little girl, than to be with another man" originates in an Elvis Presley song, but John Lennon decided to expand that into a full song. I've read claims that George really liked the song and John hated and regretted writing it.
In his last major interview, John Lennon spoke of the opening lyrics in the Beatles song Getting Better:
"It is a diary form of writing. All that 'I used to be cruel to my woman / I beat her and kept her apart from the things that she loved' was me. I used to be cruel to my woman, and physically – any woman. I was a hitter. I couldn't express myself and I hit. I fought men and I hit women. That is why I am always on about peace, you see. It is the most violent people who go for love and peace. Everything's the opposite. But I sincerely believe in love and peace. I am a violent man who has learned not to be violent and regrets his violence. I will have to be a lot older before I can face in public how I treated women as a youngster."
Speaking about Jealous Guy in 1980, John Lennon said:
"My song, melody written in India. The lyrics explain themselves clearly: I was a very jealous, possessive guy. Toward everything. A very insecure male. A guy who wants to put his woman in a little box, lock her up, and just bring her out when he feels like playing with her. She’s not allowed to communicate with the outside world – outside of me – because it makes me feel insecure."
And perhaps that would all be good and well, except that he sang the whole thing as "how he behaves when he's jealous" - it's framed as "something I did in the past" but there's no "and I don't do that any more".
