I think the primary reason is just to put a billboard up to guilt people to going to their church. But if we want to dig into the weeds:
The most likely verse being referenced is John 14:6 “I am the way, the truth, and the life. No one comes to the Father except through me.” John’s writing in nebulous Christology times, earlier gospels like Mark are rather vague about the extent of Jesus’s divinity. Jesus talks about the coming of a “son of man” who will upend the earthly power structures and make the rich poor and the poor rich. It doesn’t often sound like he’s referring to himself. By the time we get to John, decades later, and with a more mystery religion inclined author, we have the much more Godly Jesus. John equates Jesus with God in the very first sentence, and has Jesus say things like “I am the way, the truth, and the life” and “before Abraham was, I AM” (implying YHWH/Jehovah). “No one comes to the Father except through me” is an early start towards Trinitarian thinking. John is drawing on the idea of the Logos from Philo of Alexandria: God’s thoughts, platonic ideals, and/or a kind of mediator between God’s will and his creation, and personifying it in Jesus of Nazareth. This gets expanded upon by the early church into full Trinitarianism, the idea of one God in three persons, the father is not the son, the son is not the spirit, and the spirit is not the father, and all are the one and only God. The mystery of the Trinity cannot be fully understood by man, which is a great way to end violent theological disagreements while leaning on a wealth of existing Jewish and Christian and Neoplatonist tradition to do the heavy lifting for you.
Fast forward to the Reformation. Squables about fees paid to the Catholic church to cancel out sins and clear the way to heaven turn into obsessive rules checking and systematizing of sin and salvation in Christ. Early church arguments between Jesus’ brother James and Paul of Tarsus over chickens and eggs are repeated by Luther, Calvin, and Zwingli: do believers in Jesus who do good things and get into heaven do good things because they believe in Jesus, or because they are good people who do good things? The Reformed orthodoxy settles on an anthropology where human beings are totally depraved, and only through faith in Jesus can they be saved, a gift that they did not deserve, and one that was given to them unconditionally and without the ability for them to refuse. The idea that one can get into heaven simply by being a good person becomes a Protestant heresy, and verses like “No one gets to the Father except through me” turn into prooftexts.
Then the Reformed churches splinter into a million pieces. Most of the megachurches and small splinter groups, the most likely churches to be in the billboard business, fall into this Calvinist residue bucket. And thus a billboard saying
JESUS
the ONLY way to God
Is probably directed at Calvinist adjacent Christians, lapsed or unlapsed, who would understand and relate to the theological argument being made, while posing as a message for Methodists and Catholics, who for the most part have no idea what the Calvinists are on about and don’t care for them anyway.
