That's a very good point!
"Put up with" is an idiomatic expression that native speakers may take for granted -- but it must be learned, in the same way as "tolerate".
In fact, it would be easier for half of the world to learn the word "tolerate", from the Latin "toleratus", than the expression "put up with".
(For instance: we use the word "tolerar" in Porguese and Spanish.)
A well-known Esperantist, Tim Morley, gives a great talk on phrasal verbs (which, Esperanto having none, tend to trip up English speakers learning it). Here it is in English: https://youtu.be/eQ_hXML4nWg?t=671 (I highly recommend the first half of that video too, on "quite", for its humor value.)
to put (a person or animal) out of (his or her) misery
Cricket. (a) (Of a fielder or wicketkeeper) to hit or break (a wicket), dislodging a bail;
to put one's feet up
[1] http://www.longmandictionariesusa.com/res/shared/vocab_defin...