How to justify not using a certain program or API or framework because it is not free I am trying to write a justification as to why some tools were discarded in my project. My reasoning is that if I have 10-20 tools that more or less solve the same problem, and I have no clear insight on which one may perform better or any other characteristic like that, some kind of explanation as to why choosing one over the others is the right approach: some are simply not compatible to my particular project and others require payments. I talked with my tutor and I was told to evaluate the options, present them, and then pick one that would better fit the project. 

But money was, and still is, a limitation, since there is no financing for the project, not for 10$ nor for 1000$, since we don't really know how they'll behave beforehand, one limitation in order to pick a tool was money. 

What I am doing is write a state of the art of the different options, explaining different characteristics about them: how they work, what they require, and also how they are sepparated in terms of monetization. There is open source, there is what I would call, for lack of enough vocabulary, rental of the tool, you pay per minute used, and there is contracting of services which is a model that does not even offer a price, they offer you to get in contact with them and get to an agreement.

Is this a valid explanation? Am I looking wrong at the problem? Thanks in advance for the input.
Most of the reasons you gave in your post seems justifiable enough. I'll just list them to make it clear. 


You have sufficiently abled tools to solve your objective without the proprietary tool. 
You don't have a funding to cover the expense of certain proprietary tools. 
You are able to use limited licensing to cover up most of the commercial options.   


Apart from the good excuses, you could at least request the tool provider to see of they would sponsor you with a temporary research/student licence (or a similar sort) by stating your objectives.