Christianity CAN claim absolute truth, because born again Christians CAN know the will of God.
In the time before Jesus Christ, the will of God was known by the priests and by personal visitations by God. After Jesus Christ died (sacrificed) Himself for us, the barrier was broken, and men could know God personally, and know His will. The Comforter (the Holy Spirit) that was sent to us when Jesus returned to heaven shows the born again the will of God.
We are called the sons/daughters of the Father for good reason; we walk with Him as sons and daughters.
For a verse that talks about the Holy Spirit, go to John 16:12 NIV (Jesus is telling His disciples He has more He wants to tell them, but they aren't ready yet).
In John 16:13 NIV, Jesus talks about the Holy Spirit coming to lead the disciples in the will of God (The Holy Spirit will guide Christ's followers in truth; just a quick Greek note, the word guide seemed to have been used in the sense of to teach, to give guidance to, to "lead on one's way"
http://bible.crosswalk.com/Lexicons/Greek/grk.cgi?number=3594&version=nas This verse gives the Greek reference.
http://bible.crosswalk.com/Lexicons/Greek/freqdisp.cgi?book=joh&number=3594&count=1&version=nas
This verse gives the Bible verse in the book of John.
(the verses from the lexicon are from the New American Standard Bible.)
Therefore, the Holy Spirit was going to, and does, guide people by teaching them.
What is it He teaches Christians? That's answered in John 16:13 as well;
Jesus says that He (the Spirit) will only speak to the Christian what He hears. Direct quote from the Scripture (NIV, John 16:13, the last part of the verse; "; He will speak only what He hears, and He will tell you what is yet to come." We can know the will of God, because the Spirit (who a person of the Triune God) communicates to us the will of God.