A common, yet unforgivable argument against the Trinity is to cite a Bible verse that shows the Christian faith is monotheistic (Deuteronomy 6:4, for example), and say that, therefore, there cannot be 3 Gods. I say unforgivable, not in the sense that it is such a grievous sin that anyone who makes it will necessarily spend forever in Hellfire, but in the sense that whoever makes such an egregious error has proven, beyond all reasonable doubt, that they have no clue what they are talking about.
Imagine, if you will, we meet an ambidextrous man. If you aren't ambidextrous yourself, it's quite hard to imagine. As a righty, I can't even imagine being left handed. To be able to use both hands equally, for any task what so ever, would be quite amazing. But suppose I'm in a bit of a contrarian mood. Upon finding out this man is ambidextrous, I scoff at the idea. How can this man possibly be ambidextrous, given that I can quite clearly see him writing with his right hand?
I take it for granted that you see the flaw in this argument. The whole point of being ambidextrous is that you are able to use both hands. Thus, to see a man writing with his right hand does not prove he is not ambidextrous. Rather, writing with his right hand is half of the evidence that he is ambidextrous.
In much the same way, the starting premise in any argument for the Trinity is that there is only one God. The doctrine of the Trinity is inherently Monotheistic. If the Father, Son, and Holy Spirit, were 3 separate Gods, God would not be a Trinity. Rather, there would simply be 3 Gods. But the Bible says there is only one God. "Hear, O Israel: The Lord our God, the Lord is one." as Deuteronomy 6:4 says.
Rather than disproving the doctrine of the Trinity, the doctrine of the Trinity is the only way to account for the simple fact that God, who is one, exists in 3 separate persons. Scripture very clearly identifies the Father as God (e.g. John 6:27), the Son as God (e.g. Hebrews 1:8), and the Holy Spirit as God (e.g. Acts 5:3-4). Yet, these three persons are not synonymous. The Father is not the Son or the Spirit. The Son is not the Father or the Spirit. The Spirit is not the Son or the Father. This is seen in how they interact with each other, such as the Son speaking of the Father's authority (John 12:49), and the Spirit speaking on the authority of the Son (John 16:13-15).
Now, if these three separate beings are separate entirely, then there are actually three Gods. Yet, this is impossible, as we are told repeatedly throughout Scripture that there is, always has been, and always will be one God. Thus, if there is only one God, yet there are 3 separate beings who are identified as God, then these 3 beings must be one God. The Father is YHWH. The Son is YHWH. The Holy Spirit is YHWH.
All of this means the Trinity is inherently monotheistic, and therefore, any argument against the Trinity on the basis that there is only one God is as illogical as saying a man cannot be ambidextrous because he has been seen writing with his left hand.
There is more to this, of course. It cannot be denied that, as straight forward as the doctrine of the Trinity is, it is also incomprehensible. This isn't surprising, given that "...as the heavens are higher than the earth, So are My ways higher than your ways, And My thoughts than your thoughts." (Isaiah 55:9). Is the God who created, maintains, and even intimately knows the stars, supposed to also be so simplistic that if anything seems difficult to understand about Him, it must therefore be a heresy that was apparently invented by the Council of Nicaea? Of course not! Just because we're too small to understand the Trinity does not give us the excuse to deny the revelation the Lord has given us about Himself. Just as I, as a righty, cannot comprehend ambidexterity, yet ambidextrous people genuinely exist, so also can we, as monads, not understand the Trinity. Yet His word tells us, quite clearly, that He exists. This is why we get baptised in the name, not the names, of the Father, the Son, and the Holy Spirit.