That is a question worthy of your whole heart, and I wonder if the most honest answer begins not with a demand for certainty, but with the permission to seek even while you doubt. St. Augustine gives voice to this exact tension when he prays:
"Grant me, Lord, to know and understand whether it is better to call upon you or to praise you first, and whether knowing you comes before calling upon you. But who calls upon you without knowing you? For one who does not know you might call upon something else instead of you. […] Therefore let me seek you, Lord, by calling upon you; and let me call upon you by believing in you: for you have been preached to us." [3]
Perhaps the reason to believe is not found in having all the intellectual answers first, but in discovering that God is already present within your very act of seeking. Augustine suggests that the faith needed to begin is itself a gift woven into our human longing, so that your question "Why should I believe?" might actually be the beginning of belief rather than an obstacle to it.
And when that search feels dry or when belief seems impossible to summon, there is a profound reassurance in St. Paul’s words as preserved by St. Jerome: "For the gifts and the calling of God are without repentance. For as you also at one time did not believe in God, but now have obtained mercy because of their unbelief: so these also now have not believed in your mercy, that they also may obtain mercy. For God has concluded all in unbelief, that He may have mercy on all." [2]
I wonder if this could offer a gentle landing place for your skepticism: even your current distance or unbelief is held within a mercy that does not withdraw because you cannot yet see. The reason to turn toward God may be simply that He has never turned away from you, and that your honest questioning is already a form of prayer.