Why not?
I've been reading a book lately that talks a lot about that
Some major objections to Calvinsim are...
1. God's sovereignty vs. freewill.
2. Who actually are the 'elect'.
3. Calvinism would make a 'real' need to evangelize invalid.
4. God wouldn't choose only some, but would choose all. 'He desires that all...'
5. How can man be considered 'guilty', if he never had the option to choose God.
6. The atonement can not be limited, because that limit's Christ.
Obviously there are more objections, and one line doesn't do these arguments justice. I would say that if you are looking into Calvinism, these may be some of the areas you should study in the Word...not for argument's sake, but because they are valid questions. I suggest that you try to pull up the TULIP, before you accept it...be a Berean!
Freewill has been mentioned here, and I just want to give an overview of my opinion. I see God's sovereignty throughout Scripture. I think our culture struggles to think in corporate terms, and has a difficult time seeing ownership and submission as anything good. Our Creator owns everything, and we are His vessels to be used as He determines. A King is not King of a democracy. The divine love laws were not 'of the people', but rather God's sovereign decree for his people, a Jesus obeyed them, even to death on the cross. In this case, big government truly does know what's best for us, God loves us, and knows exactly what we need, more so than we do....I am pointing out the obvious.
Our will is not free in a libertarian sense. First, we are created beings, and our vantage point is from that of a created being...we just have limitations by nature. Secondly, we are post-Adam humans, fallen, and our free will is pressed upon by sin right from our birth. As we grow, we grow in sin. It deceives and hardens our hearts, which causes us to become even more pressed upon by sin...it's a cycle winding us deeper and deeper into the muck of sin and self-righteousness...we are slaves to it. God freed us from this slavery. Our will is never 'free' as we define the word, but one day it will be completely free in sense that we can serve God as we were created to do, which will be our highest fulfillment.
The Holy Spirit, Who regenerates, can give our dead souls life, quicken us, which makes us dead to sin. In this way we 'see' our fallen state...this brings the believer to a true place of repentence. Once our eyes are opened, we are then able to 'see' the Truth and grow in obedience to Christ, and 'in Christ', performing the good works God has prepared for us.
Scripture does tell us to 'choose' to 'walk worthy' etc. God uses our will, He works through it, in the same way He works through our prayers to accomplish His will. I do think there is mystery in all of this, and so I don't want to say that I absolutely have this all worked out...I don't. I keep revisiting my beliefs the same as every believer, and I try to continue to approach the Word with the hope that God will teach me. I guess, I'm not longer married to it, even though I still believe it. God is so amazing, and His thoughts so vastly higher, that He can, and will, work His plan in the midst of what we see as contradictions.
There's so much more that could be said, but we each have to work out our own salvation, and study for ourseves so that we can be approved by God, and also be used in the way He desires. The Lord bless you.