This breaks down very quickly as you get more abstract.
人 = person "rén"
门 = gate "mén"
们 = plurality marker "mėn"
也 = also "yé"
他 = he "tā"
他们 = them "tāmėn"
One can come up with a story for why person + gate is plural, but the inclusion of gate in the character for plurality is really more about the sound of gate.
This is even more interesting because prior to the 1920s 他 was a gender neutral third person pronoun. And in ancient Chinese 也 was probably pronounced differently to today's yě, perhaps more like the ā of tā. A great resource for looking up the history of individual characters is Wiktionary:
Wiktionary is neat because it also shows you pronunciations in several different Chinese languages (Mandarin, Cantonese, Minnan, Hakka etc) and the relationship to Japanese, Korean and Vietnamese, if it's there.
Yes totally. I wasn't contradicting GP. The pattern where part of the character indicates the sound is so common that it helps me a great deal when reading Chinese. My speaking/hearing is better than my reading. I might not know how to write a particular character but, if I can guess the sound, then that plus the surrounding context are enough for me to know what the word is.
木 = tree
森林 = forest
And:
田 = field
力 = strength
男 = man (because he labours in the fields)