There are two main ways anti-Trinitarians argue against the Trinity. The first is to simply not understand it. They don't argue against the actual Trinity, but against a version of the Trinity no one actually believes in. The other way is to understand what the Trinity is, but not understand how it could be true.
The latter is called the Incredulity fallacy. That is, arguing from one's inability to either understand or accept a certain viewpoint. One important thing to remember is that human beings are neither omniscient, nor infallible. We have a limited understanding.
I was thinking about this with my dog the night before this article was originally written. I ask him "do you wanna go out?" in a particular tone of voice, which makes him either run towards the door, or look at me like "do I have to?" But when I asked him without the tone of voice, he suddenly didn't understand it. He just cuddled me like he did when I said literally anything to him. He did not understand my language. A dog will never have a full grasp on the English language. It won't understand our society. It couldn't even begin to comprehend our technology. As a matter of fact, neither do I. This computer I'm currently working on is way beyond my mental capacity. Yet, the computer exists.
The distinction between man and God is far greater than the distinction between me and my dog. Just because we cannot understand the Trinity does not mean it's not true. It means we don't understand the Trinity. Yet, this is what God has revealed to us. He has revealed that there is only one God, yet He has revealed that the Father is God (e.g. Philippians 1:2), the Son is God (e.g. John 1:1), and the Holy Spirit is God (e.g. Acts 5:3-4). Three distinct, personal beings are identified as being one Holy God. Therefore, we have the Trinity.
This is very important. You cannot be saved without confessing Jesus as Lord. That makes the Trinity an essential issue. You are not a Christian if you are not a Trinitarian. Therefore, accept the Trinity, even if you cannot yet comprehend it, because you will eventually face Him, and He will judge you.