Is it true that it is absolutely impossible for some people to live without meat or is it my personal feeling of lack of satiety without at least some kind of meat product?

"Impossible" is a challenge, not a sentence. You can change your habits, and I know how.
Feelings depend on hormones, and hormones are chosen by microbes living in the gastrointestinal tract, especially in the duodenum. The most greedy microflora loves protein products, because the one who is obsessed with protein grows stupidly faster in the intestines.
Changing the diet is possible, but first you need to decide what kind of food addictions you want to get. (Not possible)
The gradual transition is to increase the proportion of new food for feeding new microflora for this food.
The consolidation of changes occurs in 2 weeks, that is, it is better to take steps so small that willpower is enough for 2 weeks ... The first six months will be the extinction of the old microflora, accompanied by fragility. The new microflora takes its final volume in about a year, that is, for the second six months it will gradually "release".
If you want a sharp transition, then it seems to me that you need to start with sports, not food. First you need to remove excess dirt through sweat, and due to cleansing, endurance will increase. Having pumped endurance, we arrange drought for microbes. Fasting can be used to achieve exhaustion, but the same effect can be obtained much more quickly with exercise. 3 or more hours of continuous exercise finally deplete the old microflora, after which food addictions remain only in the head, and the feeling of discomfort is replaced by a simple feeling of emptiness. After such exhaustion, you can even starve, and when you decide to break loose, choose raw food, or even better, juicy fruits to feed new microflora. Better sweet fruits to return glycogen to muscles. And sweet fruits do not inhibit detoxification.

It is a habit not to gorge itself without meat. Who can not eat without bread, and someone does not drink tea without sugar.

Meat can be easily replaced with any product rich in animal protein, such as cheese, cottage cheese or eggs. If desired, you can completely abandon animal food and get protein from soybeans or beans, but then the diet should be more varied, because vegetable proteins do not contain some of the amino acids found in animals.

I'm certainly not an expert, but it seems to me that everything lies in the characteristics of your body. Probably, he needs exactly those substances that are in meat. In no case do not self-diet, it can end very badly. If you have already decided to give up meat, then get tested and consult a good nutritionist who, together with you, will select the most optimal diet for you.

From personal experience, I can say that after giving up meat, I gorge myself on a small plate of vegetables / cereals / potatoes. I think you just need to practice vegetarianism for longer, so that there is a definite conclusion applicable to you.

In other words: try not to eat meat longer.