We believe we are saved by grace through faith as well. But that faith is God's gift as is proven by Scripture Php. 1:13, Rom 10:17; Romans 12:3; 1 Cor. 4:7; 1 Corinthians 1:22ff and the faith we have is only by the power of God, not ourselves, see Eph. 1:19 carefully.
1) First, if faith in Christ is instilled via irresistible grace, we are saved by grace and given faith. Not how it reads. To be saved through faith, means our faith existed before we were saved, like entering a room full of grace through a door made of faith. We go through the door to gain access to the grace in which we stand, Romans 5:2.
2) Philippians 1:13-14 refers to "brethren trusting in the Lord because of my imprisonment (or trusting because of my bonds)." No support whatsoever for trusting because of irresistible grace. Yet listed as if it did. So a disingenuous reference.
3) Romans 10:17 says faith comes from hearing, not from irresistible grace. Two for two, no support whatsoever for "the gift of faith." Second disingenuous reference.
4) Romans 12:3, at least mentions something that could be misinterpreted as the gift of faith. The verse says we are allotted "a measure of faith." .” What is asserted is that this measure of faith is allotted before salvation and is the means of salvation. But lets look at the context and see if we can figure out what Paul is actually saying. Each one of us, who is saved and indwelt with the Holy Spirit is gifted to build up the body of Christ. But we are not all given all the same gifts, for some are teachers, and some are leaders and some are servants. Each has been allotted a measure, a sphere of influence, an area of calling so that together we can build up the body of believers until we all attain the unity of faith, which is to be Christ-like. So rather than pre-salvation faith, the idea is our post salvation Holy Calling. Although mistaken, at least this verse could be construed to support irresistible grace.
5) 1 Corinthians 4:7 says everything we have, including our faith, we received. But it does not say or suggest we received faith by irresistible grace. Since faith comes from hearing the word of God, we received our faith through the call of the gospel. So we now have 3 or 4 disingenuous references that provide no support whatsoever for irresistible grace.
6) 1 Corinthians 1:22, here the idea, not in the verse but in the passage is that is that gospel is foolishness or a stumbling block to those that do not believe. Again, it does not say nor suggest those who believed were altered supernaturally by irresistible grace.
Bottom line: Four references are non-germane, and one provides an ambiguous phrase that Calvinism misinterprets. Go figure.
BTW, Ephesians 1:19, read any which way including "carefully" says the power working in and through us who believe is the same power that raised Christ from the dead. Again, no support for irresistible grace giving us faith before we are placed "in Christ." None, zip, nada.