Why did Latin poets make metre and word stress clash on purpose?

Because classical Latin verse was not built on stress, which left word stress free to be set against the beat. Unlike English verse, ancient Greek and Latin poetry is based on the length, the relative duration, of a syllable, and in scansion word boundaries do not matter. Latin words still carried stress, and poets arranged their lines so that the two would disagree or agree where they wanted.

The line they played on is the dactylic hexameter of Homer and Virgil. A dactyl is one long and two short syllables, named from the Greek for finger, after the long and two short bones of a finger. The first five feet of the line are a dactyl or a spondee, two long syllables, and the sixth is a spondee or a trochee. Virgil opens the Aeneid with one: arma virumque canō, Troiae quī prīmus ab ōrīs, "I sing of arms, and of the man who first from the shores of Troy."

Here is the clash. In Latin, lines were arranged so that the metrically long syllables at the start of a foot often avoided the natural stress of a word. In the earlier feet of a line metre and stress were expected to clash, while in the last two feet they were expected to coincide. In Virgil about 85% of lines have a word division after the first syllable of the third foot, which, because of Latin's penultimate accent, ensures that word accent and metre do not coincide there.

The pay-off is rhythm that acts out the story. A Virgil line describing galloping horses is five dactyls and a closing spondee, an arrangement that imitates the action; a line for the blacksmiths forging Aeneas's shield has five spondees and word accents cutting across the verse rhythm to give an impression of huge effort. English poets who tried the metre, including Longfellow in Evangeline, wrote mostly accentual versions rather than quantitative ones.