The Silence set out to kill the Doctor to prevent him from ever saying his name on Trenzalore, as something bad would obviously happen there, hence the phrase "Silence will Fall." Although it hasn't been revealed, based on deduction, the Silence must have been trying to stop the Great Intelligence from getting into the Doctor's timeline and making all his greatest victories into failures, which would ultimately lead to the death of billions, if not trillions, of beings within the universe. Thus, it would seem plausible why the Silence didn't want the Doctor to reach Trenzalore to stop such a disaster from happening.
However, the Silence could only have set out on stopping the Doctor from reaching Trenzalore after the events of "The Name of the Doctor," meaning after the Great Intelligence had already crossed into the Doctor's time stream - basically creating another paradox by preventing the Great Intelligence from altering time by killing the Doctor. Although if it was after the events from "The Name of the Doctor," then surely they would have been aware that, at the same time the Great Intelligence goes and alters the Doctor's timeline, Clara jumps in moments after and most likely manages to prevent the Doctor's time stream from altering, meaning all those lives he did save remain saved.
If this is so, then why did the Silence then need to go and and stop the Doctor from reaching Trenzalore, as the only plausible reason was to stop his name from being uttered in the TARDIS - the one that becomes bigger after his death - which would open up the "tracks of his tears."
But, Clara stops the Great Intelligence, so then why did the Silence need to go and stop this from happening as time still remains the same following the events of this episode?