Breakdown of Eles tentam explicar o motivo, mas não quisemos ouvir.
não
not / no
eles
they (m)
mas
but
querer
to want
Questions & Answers about Eles tentam explicar o motivo, mas não quisemos ouvir.
How do we form the "we" past tense of querer here?
Querer (to want) is highly irregular in the Pretérito Perfeito (simple past). For "we" (nós), it becomes quisemos. Notice how the stem changes completely from "quer-" to "quis-". If this were the present tense ("we don't want"), it would be não queremos.
Why does the sentence start in the present tense (tentam) but end in the past tense (quisemos)?
This shows a contrast in time. They are trying to explain right now (or as a general ongoing action: tentam), but our refusal to listen happened at a specific completed moment in the past (não quisemos).
Why is there no preposition between the verbs in tentam explicar or quisemos ouvir?
Does motivo just mean "motive" like in a detective show?
It can, but in everyday Portuguese, o motivo is simply the most common way to say "the reason" why something happened. You might also hear a razão, which means the exact same thing in this context.