Could you show us in the scripture ( that we all agree is the word of God) where Jesus or the apostles ever taught the church could or would teach infallibly?
Sure, these verses(among many) illustrate that Christ would provide His people with a source of the truth of Revelation and this conduit would be His Church. Christ, being true God and true man knows us better than we could ever know our selves: He knew that we would need a guide, like the eunuch that Philip instructed, in our race. When God promises, He delivers, we may not like the way He delivers it, but it doesn't change the fact that He has and always will make good on His promises.
Matthew 16:18 And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.
Luke 10:16 He that heareth you heareth me; and he that despiseth you despiseth me; and he that despiseth me despiseth him that sent me.
John 13:16 Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, that shall he speak: and he will shew you things to come.
John 14:16-17 16And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever; 17Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.
There are many other verses, look HERE