I'd suggest reading What is Reformed Theology? by RC Sproul if you want to accurately understand Reformed Theology.
The anti-Reformed people here will likely inaccurately represent it, and also you won't get the Scriptural support for it, which is in abundance. I would particularly suggest reading John 6, Romans 8-11 and Ephesians 1-2.
I do not believe the infant baptism part of Reformed theology, and I think their view of the covenants is oversimplified, but in essence I am in agreement with it.
I was in agreement with it before I knew what it was called, simply from reading Scripture. I remember my Arminian pastor telling me I was a Calvinist when I explained to him why I felt his teaching was off base on some topics, particularly eternal security.
Anyways the Arminians will argue this one to death, but ultimately God is sovereign in all things, and is the author and finisher of salvation. All glory and honor belongs to Him, and self is not our co-Savior. I rarely see non-Reformed people talking about the transforming power of the Holy Spirit, and that is indicative of a problem. I don't acknowledge either Mary OR self as a co-Savior, and to be honest Arminianism, to me, is very much a return to the thinking of Rome (Catholicism lite, without the pope and indulgences and Mariology). I didn't initiate my salvation, nor will I complete it..it is totally a work of God.
Also, the caricatures of being a robot are a joke. Calvinism doesn't teach that. We freely pursue sin prior to salvation due to a fallen nature, and we freely pursue righteousness after salvation due to the new nature. It can be said that we are slaves to sin, in a way, prior to salvation because we freely pursue it out of necessity due to our fallen nature, but when I say this, I am only saying explicitly what Scripture says.
I am not a big fan of the word Calvinism by the way...I prefer Reformed theology or monergism. Calvin wasn't the founder of Reformed theology, neither was Augustine. It is derived systematically through studying Scripture.
Anyways, if someone wants to HONESTLY study Reformed theology, I can suggest RC Sproul's book What is Reformed Theology? as an introduction, then some of James White's books such as Potter's Freedom or Sovereign Grace for more advanced understanding. If you really want to see a good example of the futile arguments of the opposition, read the book that he did debating Dave Hunt called Debating Calvinism: Five Points, Two Views.
Basically Hunt's argument was, if Calvinism is true, God is not loving. Which is the common argument from Arminians. They think that they define the parameters of God's acceptable behavior by their human standards, rather than allowing Scripture to speak with regards to this topic. Calvinists do not judge God whatsoever...if Scripture says something, it's true. For example, Scripture indicates eternal conscious torment (or most agree with this view)....most Arminians have no issue with accepting this view, even though it is hard to comprehend how the garden-variety unbeliever deserves it. They also have no issue with God destroying entire families for the sins of the family head (Korah, Dathan, and Abiram, as well as Achan in another incident), even though that violates the human concept of "fairness". But, when it comes to Reformed theology, all of a sudden they have a problem because they think election is "unfair"...that God would save some rather than all. I would remind them that the fair thing is that all go to eternal punishment due to their sins, and that it's only by God's grace that ANY are saved. Our Western entitlement mentality chafes against this, but it is true.
In addition, I actually think that Reformed theology is more fair in a way than the Arminian view. If God sovereignly elects people out of all nations, He makes absolutely sure they come to faith, regardless of anything that may be a barrier. For example, I have a friend in Saudi Arabia who came to Christ. God provided him a dream AND a former missionary to Muslims to guide him to Christ. Hearing his testimony was a very emotional experience for me. He had ABSOLUTELY no intentions of becoming a Christian; in fact my understanding is that he was in language school so he could become a jihadi and God gave him the dream during this training..so there was absolutely nothing about him pursuing the Christian God which merited his salvation. It wasn't his "fault" that he was raised in an environment that taught him to hate the one true God...God's grace overcomes all such obstacles...but according to the Arminian frame of mind, salvation is ultimately about you having enough residual righteousness to make the appropriate response.
So, in general, I think election is more fair to individuals like my friend, who through no fault of his own was born in a culture hostile toward Christianity, without the benefit of Christian parents, with the odds heavily weighed against him coming to the Christian faith. God is able to save anyone out of any environment through his sovereign grace.
Read Daniel 4 and see if Nebuchadnezzar had such intentions...notice how God brought Nebuchadnezzar to submission, and broke his foolish pride..Nebuchadnezzar ended up praising God as a result. God knows each person inside and out and can bring them to full repentance if he desires. To deny otherwise is to deny God's omniscience, omnipotence and power. The question is, why isn't He doing so? Election explains that well for me.
Just a few thing to think about..I'm sure the Arminian side is producing their own arguments, largely based on philosophical assertions.
By the way, if this falls back to John 3:16, Reformed theology wholeheartedly acknowledges this verse..who has faith but the elect? God provides faith as a gift to those who are redeemed (Ephesians 2:8-10). Regarding phrases like "all men", if you read the context, these remarks are largely meant to point out that not only Jews are going to be saved, but also Gentiles. Regarding other "difficult scriptures", consider who the audience of the letter is...is it talking about people within the church, or the world? A lot of the Scriptures Arminians will point to have a specific context, and the context is not being considered in their explanations.
So, whether I like it or not, from a human perspective, I think Reformed theology best reflects the biblical teaching. I believe there may be some missing piece to the puzzle which may more fully reconcile some of the troubling issues involved with it, but in essence it is the best SYSTEMATIC theology. Until something better comes along, which surely isn't Arminian theology (I find their exaltation of man's autonomous free will to be disgusting and dishonoring to God), it's the systematic theology I embrace.
In addition, Reformed teachers are generally very faithful to presenting God's word. Everything they believe, they support with Scripture, and they have an exalted view of God's holiness and sovereignty. I cannot say so with the Arminian camp, where several really bad teachings are rampant in the church..I could name several of these bad teachings but I will defer