Welcome to the community, and thank you for adopting this Moluccan, one of thousands in shelters and rescues across the US and the world...
Now, you need to take a step-back and think about some things for a minute...First of all, and most importantly, you've only had this Moluccan Cockatoo for a month...A month is like a second in bird-time, especially a Moluccan Cockatoo that has been re-homed probably multiple times...You didn't give any history about your new bird, at least what you know or were told, such as how old is your bird, was your bird DNA-tested for gender, and if so, what is your bird's gender, how many prior owners has your bird had, how long was your bird in the Rescue/Shelter, and what is your bird's regular, daily diet? This is information that will help us to help you...
Regardless of the anything else, it's quite obvious that your bird is still not entirely comfortable in your home or with you, which is to be expected. Your bird has not yet given you his trust, which is also to be expected. And until you fully earn the bird's trust, the bird is going to exhibit a lot of territoriality, dominance, and just plain skepticism and distrust. That all being said, by-far the most important thing that you need to stop doing immediately is "forcing" your bird to come out of their cage the way that you have been doing. If you keep forcing your Moluccan the way that you have been with regards to his cage, you will never earn your bird's trust, he will never want to willingly come out of his cage whenever you open the door (which is what should eventually happen, but should not be expected to happen any time soon), and your relationship with your bird will only regress and become volatile and eventually aggressive.
Right now you are in what is know as the "Honeymoon Phase", and with parrot that has the intelligence of a 4-5 year-old human child like your Moluccan has, if you continue to force him to come out of his cage every day, with your hands inside of his cage, his territory, the "Honeymoon Phase" is going to end very quickly, and when it does you are going to have a very serious, huge problem...You are expecting way too much of your bird after only a month of being with you and in your home, and you need to stop and instead of going at "Your Pace", you absolutely must go at the "Bird's Pace". If you don't go at your Moluccan's Pace, especially with regards to his cage, he is going to become aggressive, unable to be handled at all, he'll never come out of his cage, and when you do put your hands in his cage, he's going to attack them and hurt you.
You said that you "don't understand what it is with his cage", and that's a really big issue...I wrote a post yesterday or the day before to a new member having issues with his Cockatiel, and I'm going to go find it and then copy and paste it in another reply below for you to read. It's all about birds and their cages/stands and the the relationship between "their territory", their new Flock (which is now you and anyone else who lives in your home), dominance, and respecting their "safe space", which in the case of your Moluccan is inside his cage....I'll post it below, disregard any specific reference to the other member's cockatiel, and pay attention to what I say about their cages/territory, the location of their cages in your home, and their "flock", and the relationship between all of these...It will answer your questions regarding why your Moluccan is acting the way that he is about his cage...
***You need to to stop doing what you have been doing as far as forcing him out of his cage...You said "it's like a little game to see who will give in first", but to your Moluccan this is not a "game" at all, to your Moluccan you are reaching your hands into his territory, his only "safe space" that he has in the world, and you are physically forcing him to come out by actually "grabbing his foot"...None of this is good, and even though you mean well and are just trying to get him to come out of his cage, if you keep doing this your bird is going to eventually say "okay, that's enough of this" and he's going to become extremely aggressive and very possibly hurt you. Birds learn best from "Positive Reinforcement", which in the case of a very intelligent parrot who totally understands logic and reason, means rewarding him with both lots of verbal praise and whatever his favorite food treats are; this is the absolutely best way to teach your Moluccan what you want him to learn to do (and really the only way). Right now, from your Moluccan's point of view, you reaching your hands into his cage, grabbing his foot, etc. to FORCE HIM to come out of his cage is very much "Negative Reinforcement", and in the end this is only going to get you the exact results that scolding him verbally, yelling at him, and physically punishing him with spanking or smacking him on the beak, etc. would get you...which is nothing but aggression, bad behavior, constant screaming, etc. It has been proved time and time again, over and over again, that neither "Forcing" a bird to do things, nor using "Negative Reinforcement" of any kind as "punishment" when a bird doesn't do what you ask them to do will completely fail to achieve the results that you are trying to get in the first place, and only results in MORE bad behavior from the bird...So you really do need to take a step-back here, because you have been simply expecting way too much from him after only a month, and honestly you are being quite brave, yet maybe a bit wreckless, by taking him out into stores and such with you already, as it's quite obvious that you have not earned the bird's full-trust yet, nor is it expected that you would have. This is not a new Dog that you adopted at the SPCA, this is a Moluccan Cockatoo, probably the most-intelligent of all parrots, period. And this is a Moluccan that has been yanked from at least one home, his first home, and he has not been given ANY REASON to trust human beings at all, just the opposite...So you really do need to slow-down and go at HIS PACE, not your pace. Work on your interactions with him at home first, a little training using only Positive-Reinforcement at home every day, before you start taking him into the Grocery Store or Pet Stores with you, and certainly before you start reaching your hands into his cage, grabbing his foot, and physically forcing him out of his cage...