Hi Powereng,
I think you rushed to respond and you did not show that you are able to do whatever it takes and show them that you tried/trying harder.
Then, they can help you out. And another thing is that if you love Quebec and want to stay there, acknowledge that at some point they will have some unfair decision regardless of being a developed country.
I tell you my own story, it is not the first time I apply to Quebec. In 2010 I was still doing my bachelor's, then I had an application in process with Quebec, we were not required to provide any language test at the time. Where you come from and where you studied your degree and your work experience you had could determine your points of acceptance. After my graduation, I updated my application with my degree excited that I am going to Quebec in 2012. Guess what, the decision was made without considering my degree in computer science and I was not even given the opportunity to defend myself, because the argument was around my degree and the little work experience I had, which one could have been considered (not both) - some messed up things like that. I applied for a review because at the time I applied, there were no such rules and there couldn't be used against my application. At the time it was taking forever to make an administrative review, and I gave up and withdrew my application, but I learned that the Minister has given a green light to my application if I would have waited for a little time they were about to send me the CSQ. They added, if I am still interested in Quebec, I can apply again and submit a new application from scratch. I went straight to the Minister, and I told her the truth that I was exhausted and at the time I was studying abroad and it was hard to deal with immigration, school, and life in general. Then she put a condition to my face - if you take a French test and get B1 at least I will give you the CSQ (this came from the Minister's cabinet). Being graduated in a foreign country, and looking for jobs, I had no money for the French test or time to prepare for it to save my CSQ. The good news at the time, I had the opportunity to go somewhere else and it was less torturous. And here again, I am doing it from scratch.
I learned one important thing, you can argue about unfairness as much as you can, but it will just hurt you more. And sometimes there is a light in our path and we (the majority) ignore it. The truth about Administrative Review, they only look at the information that was available at the time the agent made a decision. To me now, I see that you have even closed that door the Minister could have acted on. Guess what, Administrative Review will just look at the points you are claiming above and say you do not have sufficient points. This is completely different from the following, "I see your effort and I am confident that you are going to do well in Quebec". You could have waited for your degree and taken an English test. You are in Quebec, if you could have taken French and gotten even A2 it would have made a big difference (not points for the French, but the effort and willingness to align your vision with the government requirements - it is a ticket itself).
Another thing you have to know, these guys at MIFI operate on a sheet, they check what you have provided against that sheet. If nothing, they make a decision accordingly, and they have no power beyond that. Your request to forward your application to the Minister, it is not for them to do. Your job here was to give them the strongest application ever with your maximum effort. Then during the administrative review, the Minister can have the opportunity to let you pass. This is how you make it from what I have seen around the World. And another thing you ignored that I am seeing now, using a lawyer in a situation like this is handy because instead of going that the agent made a mistake, you could have sent a nice explanation letter saying about your discoveries. Trust me, even if they have access to all information, it was your opportunity to provide evidence that you have been in the country that amount of time you are claiming, the region where your job offer is - a printed document from the immigration website you are referencing to, a letter of service that the Main applicant has been working full time more than 6 months. This alone could have saved you.
If I were in your shoes, I would seek help (a lawyer) and alternatively, take the English test and create another Arrima account for a new EOI if possible - I have no idea, but not only in hope with Ministerial Discretion. One thing you could have done for sure, you let them reject a strong application. That's it.
I hope things will get better in the end.
Cheers,
V.