Why doesn't human consumption of plants cause infectious diseases the way consumption of animals can?
If you mean if there are viruses, pathogenic bacteria or fungi that may cause diseases both in plants and in animals, the response would be that this is very unlikely (But even so, some fungi and bacteria could do it if some circumstances are given). This is due to some key factors:

First of all, the philogenetic distance between plants and animals is huge. Diseases transmitted by the consumption of animals are called zoonosis, and obviously it is more likely to catch a zoonosis by eating pork than eating shrimps or clams. While it's true that certain parasites have different hosts and use them to transmit themselves (for instance, many platyhelmintha uses mollusks or insects to spread themselves towards mammalian or avian hosts) parasites than have only one kind of host usually are adapted to live inside them, and they usually are unable to infect different organisms. Very few parasites can infect a human and a starfish, and even fewer can infect at the same time a human and a tomato plant.

Second, and related to the first, plant physiology differs completely from animal physiology. Plants usually defend themselves by their natural barriers (cuticles, cell walls), hypersensitive response (programmed cell death in order to limit the spread of a pathogen), isolation and/or outgrowing of the pathogen and accumulation of chemicals. Animals main mechanism is immune system. There are very different strategies and very few organisms can effectively avoid all of them at the same time. In the case of viruses, they would even have to face the fact that animals and plants have huge genetic differences.

Third even if they could, the pathogen will face competition against other pathogens that would be more specialized. Bacteria and fungi can be really hostile towards their microfoes, using a wide array of strategies. This hypothetical pathogen would be very unspecific, so they would have a hard time against more focused microbes. It should be noted, however, that unspecialized organisms usually have a great advantage if the environment have some perturbation, and they also are more resilient toward stress. Many plant pathogens are generalistic organisms that attacks when the plant is harmed or stressed. The same applies to many opportunistic infections in animals.

Despite all of this, there are some diseases that should be mentioned. Some fungi of the Clavyceps genera are plan pathogens, but they produce toxins than can affect the nervous system of animals, causing an intoxication called ergotism (the most famous of this chemicals is the lisergic acid, also known as LSD). Other fungi can produce toxins while they grow in plant tissue. Moreover, there are many fungi that can grow both in plant tissue and as animal parasites (mainly arthropods and nematodes), but in this case the plant pathogenesis usually occurs only when high fungal concentration is achieved or the plant is already damaged. While it's not a real infection, plant pathogens can cause allergic reactions. Finally, phytopathogenic fungi and some bacteria can cause infections in wounds or mucoses in individuals with a compromised immune system, but in this case the source seems to be the spores in the air.