Why does one spot of blood make the whole egg treif and make the other egg treif that I cooked with it? Why can’t they just be fleishig?

In the past, eggs were fertile unlike the eggs most of us buy today in the supermarket. A blood spot might have been the beating heart of the chick beginning to grow. Today, with eggs that are not fertile, the issue of life starting is no issue at all anymore. If you eat fertile eggs, you abide by the rules as established by the sages. But the blood of eggs is still not kosher and sometimes, you will find an egg where you don’t even see a blood spot but the white of the egg is pink from blood. That egg must be discarded.
Remember that the only eggs that are kosher are the ones that come from kosher animals—kosher birds and kosher fish. The eggs of turtles and platypuses and owls are not kosher.
When eggs are raw and to be broken for use, one usually breaks the egg and drops it into a glass dish. If you were to drop it directly onto a hot frying pan, the pan would become unkosher if the egg had a blood spot.
Consider another idea that is put forth in the Shulchan Oruch (Code of Jewish Law.) Fish blood is kosher and pareve, but if you collect it into a basin, you may not use it for food. This is because one should never create the appearance of eating or using blood. Someone might misinterpret what you are doing as using blood. The prohibition often translated as eating blood also refers to the use of blood in divination. It was a custom of other peoples to open a bird (thereby killing it) and to divine the future by the trickling pattern of the blood as it flowed out from the dead body of the bird. Using a blood egg might have created the same misunderstanding if one were to notice it. Jews were forbidden to divine or to use up an animal’s life needlessly. That’s why the pasukim (verses) contain the reminder that the life is in the blood: Lev. 7:26-27 and Lev. 17:10-14.
In some cases, the spot can be removed and the rest of the egg left intact. This is usually the case of a boiled egg. When the blood discolors the whole egg or cannot be removed without leaving a trace of blood, then the egg is not kosher. Most of the blood I have seen in eggs is so abundant that there is no thought of even trying to find a part of the egg to use. At times, there will be just a spot of blood. Usually, the spot is on the yolk, and trying to remove it would break the yolk. So that egg is not kosher.
When cooking eggs, the rule is to have three eggs in a pot at the minimum. Eggs were considered treif (not kosher) if one egg was cooked in a pot with a blood egg. If two eggs were cooked in a pot with a blood egg, they were not considered treif. Compare this to a pot of beef soup into which is dripped accidentally one drop of milk. The soup may still be kosher depending on the quantity of soup in the pot. In such cases, one should consult a rabbi.
It is not necessary to cook an odd number of eggs in a pot. That idea comes from the minimum number three of eggs that should be cooked together.
Some eggs are certified to be kosher. But this doesn’t mean they will be. You still have to check them for blood spots.
In my experience, when eggs are certified to be kosher, they have few blood spots because they have been checked so carefully. When I buy other eggs, I find lots of blood spots. And when I’ve bought fertile eggs, I’ve had to throw away so many that I stopped buying them altogether.
Do eat eggs. They are nutritious, containing some of virtually every nutrient known except Vitamin C.