1: Libertarian free will is false, therefore any denomination which assumes or dogmatically affirms libertarian free will is false. This eliminates every form of christianity besides calvinism and lutheranism. Compatibilist free will means you are free to do as you will, libertarian free will means your will is free to self-determine and determine outcomes. It is the difference between saying "I can do what I want" and saying "what I want to want determines what I do". Libertarian free will creates an infinite regress. Do you will to will what you will? Do you will to will to will what you will?
I can point to limiters of free will in the libertarian sense, things that influence people's decisions and ultimately determine what their "will" even is, however no example of an outcome determined by libertarian free will can be pointed to. The more factors I point to, the less room there is for it. Genetics, environment, nutrition, education, culture, hormones etc.
Not only that, but libertarian free will requires a mechanism that does not exist. In other words outcomes are predicated on something, and the options for what that something is do not include a basis for libertarian free will. There is cause and effect and there is randomness, neither are capable of supporting self-determined and free choices. Con must propose a third "things happen this way" type of option, or concede that only calvinism and lutheranism are viable.
2: Calvinism cannot be true because while lutheranism is an exposition and application of what scripture says, calvinism is an attempt to bend scripture to what John Calvin thinks makes sense. The result is nestorianism, making up his own theory of the eucharist based on nestorianism, and numerous examples of mental gymnastics. Lutherans believe that you should define christianity as nothing more and nothing less than what God has revealed, whereas Calvinists believe that you must shape doctrine to conform to human reason even if it means making stuff up. The heart of where lutherans and calvinists disagree is the communication of attributes, lutherans affirm that the human nature of christ can share in divine attributes and calvinists do not.
It is not about sharing ontology (besides personhood), or the humanity of christ becoming a source of divine attributes, it is about the humanity of christ being able to do things that humans can't normally do due to its seamless union with the divine logos/son. This is key to the idea that the body and blood of christ can be sacramentally present in the eucharist, not as literal pieces of meat in your mouth etc. but in a way that transcends spatial locality. In other words the body of christ can be present in two places at once, yet not divided into two. The body of christ can share in God's omnipresence, which is something Calvin (and Zwingli before him) couldn't wrap his head around so he started coping and seething, even though the bible speaks of Jesus doing many physics-defying things a normal human can't do which Calvin makes all types of excuses for. But without the communication of attributes in a real and not merely metaphorical sense, there cannot be a seamless sharing of consciousness between the human and divine minds of christ, and hence you create two separate conscious frames of reference and you create two people out of the one person of Jesus.
3: Lastly I will address the issue of sola scriptura and church authority, which is surprisingly easy. "Ecclesialists" such as catholics claim that you cannot have an infallible canon of books or infallible interpretation of scripture without the church being infallible as opposed to merely authoritative. Someone has to decide the canon right? Someone has to decide the true interpretation right? This creates an infinite regress. If you need an infallible church to have infallible scripture then you need an infallible super-magisterium to interpret the infallible magisterium that interprets the infallible scripture.
