Why do fruits have such a low protein content (with a few exceptions) ? Don't seeds need protein while growing up? In comparison, the egg of a hen contains lots of protein, used to make a chick.
If we look at just the fruits people generally eat, the fruit part is seldom (if ever) needed for the seed(s) contained within the fruit to sprout. Rather than the fruit being nutrition for the seed, it seems to be more of a lure. Fruit-eating creatures eat the tasty fruit and so disperse the seeds, perhaps contributing a packet of nitrogen-rich fertilizer. The plant thus has an evolutionary incentive to make the fruits inexpensive to produce yet tasty, so lots of sugars, few proteins.
You can compare this with flowers that produce nectar to attract pollinators.
It is don't have time to document this enough to make it a good answer but it's too long for a comment so I'll post it anyway.
A big difference between plants and animals is how they get their food, that implies they have different elements to work with. Proteins are made of amino acids, which contain nitrogen, meaning to make proteins you need lots of nitrogen. Plants get their energy from converting CO2 to carbohydrates; this is a plentiful source of carbon, but they can't get nitrogen that way. There are two ways of getting nitrogen: from the ground, and from converting atmospheric nitrogen to organic nitrogen, a process so energy-intensive that only bacteria evolved the ability to do it and only some plants use those bacteria (basically feeding them some of their hard-won carbohydrates "in exchange for" the organic nitrogen compounds).
Animals on the other hand get their food from plants, which contain all the carbon they might need and contain much higher concentrations of nitrogen than you find in the ground (the plant basically went to a lot of trouble to get all that nitrogen from a large volume of ground into its comparatively small body, or to convert atmospheric nitrogen into organic, useable nitrogen), or from animals which contain even higher concentrations of nitrogen. Note by the way that some herbivorous animals are limited by lack of nitrogen as well; I'm thinking of pollinating insects which can struggle to live off of sugary nectar alone and also need to eat some of the protein-rich pollen even though that's much less advantageous from the point of view of the plant (sugar being very easy to make for the plant but proteins much less so).
Obviously animals who eat other animals don't need to worry about nitrogen intake much at all, other than making sure they get food in general, because the animals they're eating will contain pretty much the same carbon:nitrogen ratio they themselves contain.
tl;dr: the egg contains more proteins than the seed because the chicken that made the egg ate a whole lot of seeds, and all the protein in those seeds ended up concentrated in that one egg.
EDIT: running into this much later I realized I missed a pretty vital half of the question, because there is a difference between fruits and seeds. The difference is the following: nitrogen is precious for plants so they'll try and use it for very important things. Seeds are very important to the plant, so while a seed has less protein than an egg it will still have lots of protein by plant standards. Fruits now, that's another story. Like the sugary nectar, fruits are a bribe for animals, a bit of food offered to them so that they'll spread the plant's seeds. And like with the sugary nectar, the plant has every incentive to pack that bribe full of cheap carbohydrates and as few precious proteins as it can manage.
In brief the lower protein content of a seed compared to an egg is caused by two reasons.
(1) The structural components of a plant versus that of an animal. The structural components of plant is made by cellulose which is made of glucose subunits. Animal in contrast are have large amount of muscle tissue to allow movement and much of animal is held together by collagen and keritine. All these components are different types of protein which are build from amino acid sub-units.
Hence to build a seedling you need glucose. To build a chick you need amino acids.
(2) Metabolism. A plant can build all amino acids that it needs from glucose and fixed nitrogen source. Animals in contrast are not as self sufficient. Some amino acids cannot be synthesized and must be obtained from an external source.
Hence a seed need not carry much or as varied quantity of amino acids. In fact this metabolic completeness has been used as an anti herbivore defense mechanism. Many seeds are severally deficient in one or more amino acids. Any animal that feeds solely on just one type of a seed would experience malnutrition.
An egg however has to carry more amino acids, especially the essential amino acids that it cannot synthesis from other amino acids.