Birdies, I am the mother like that. There are six people in my family whose needs must be accounted for all of the time. It is not humanly possible to keep all six happy at the same time, nor is it the best way to raise children, in my opinion. My husband and I believe that children who have every whim handed to them do not grow up to make very good adults, and that's our job; to raise good adults. It is not our job to be their buddies nor to make life a magical place where everything is happy and shiny all the time. Patience, problem-solving, and reasoning skills are all very good to have later in life, and are mostly learned through adversity.
The junior members of our family are not privy to the details of the decision-making process. We consider all of the factors before we make large decisions, and decide things based upon what is best for the whole family, not at the whims of one child or another. If a child has concerns and cares to approach us with them in a calm, reasoned, and rational manner, we will listen to them and take them into account. If, however, a child who is prone to whining anyway throws a tantrum over one of our carefully thought-out decisions, then it becomes obvious that said child is demonstrably not mature enough to be a part of any decision-making process and is in fact causing dissension and strife for purely selfish reasons. At the end of the day however, no matter how reasoned the argument, the burden to manage the household still lays on the parents and any decision is their responsibility.
Were you my child, you may not know that I'm likely to lose my job at any time and am concerned about the financial aspects of adding new mouths to feed to the household. You would probably also not be as painfully aware as your mother is that you will be most likely leaving the house in a few years. Most newly-minted adults do not find themselves in a position to be able to afford or to house livestock, leaving the animals with the parent. Your mother may not want to put either herself or some hypothetical chickens into such a position. I know that I don't lay those loads on my kids, and they probably have no idea. It's not their jobs to carry those burdens; it's mine and my husband's job.
Lest you think that I'm completely heartless, I was your age once. I wanted a horse so bad that I could taste it, but my parents vetoed the idea. I went out, got a job in the veterinary business, and was happily surrounded by animals for years. I did finally get that horse, once I was 30 and financially stable enough to afford it while being a single parent. And it was great for a few years, but such a lot of work and money. I sold her a few years later, and as much as I enjoy them now, I wouldn't take one on a bet. The same goes for my chickens; if I lose my job and can't afford to feed them any more, I will sell what I can and slaughter and eat the rest to provide food for my family, who are more important than pets or my hobbies.