Synthetic fertilizers are a non renewable resource, made from petroleum products. The use of synthetic fertilizers is unsustainable while compost is a renewable and very sustainable product and compost will give your plants all they need to grow. Since the use of synthetic fetilizers really began in about the 1950's we have lost more soil than in all the years prior to that time sinc ethe beginning of time. If we want to continue living on this planet we need to start building out soil up again of we will not sustain life on earth.
Making your own compost, recycling the waste you generate is one small step in that direction.

That's a pretty simplistic answer and not extremely helpful.

Compost is a great product but don't confuse it with fertilizer. Although it does contain nutrients, they are in very low levels and it is more accurately considered an amendment or soil conditioner. Whether or not it will provide all the nutrients your plants need for healthy growth is a bit up in the air without testing. Not all fertilizers are synthetic in origin - there are a great many organically sourced fertilizers that can provide required plant nutrients and that are easily and cheaply located. When growing harvestable or edible crops, it is often necessary to supplement existing nutrient levels from year to year, as harvesting the crops removes a lot of nutrients from the soil. Don't be intimidated by those who consider fertilizers "bad" - they do serve a very necessary purpose and one doesn't have to contribute to soil decline or pollution by using them - synthetic or organic - in moderation.

Keep an eye on your garden to assess growth. If the plants appear to be discolored, stunted, struggling or not producing as they should, you may need to supplement.

Thanks for the info Love my Dad but it would be nice to just see him eat crow.The land my garden is on is so poor that it wouldn't even grow vegetables with synthetic fertilizers.

Your dad's view of 'fertility' is one that was started when the chemist Liebig discovered which chemicals, or molecules, were required for plant life and health. It was information worth knowing, and the fertilizer industry grew up around the idea that they could provide those molecules for a farmer.

"Organic" techniques had been observed, but were not understood, and in the absence of an understanding of organic techniques, and in the face of proven success with chemical supplements, fertilizer addition was the usual mode of farming.

Even now, over 125 years later, are we still learning exactly how organic techniques work. Mycorrhizal relationships are still being explored and researched. CEC and chemical buffering are still somewhat mysterious to many farmers. The concept of the 'food soil web' is still considered airy-fairy despite its very scientific basis. But No-till techniques that leave plant residue in and on farmland are the newest technique in corn and bean production.

The term 'fertilizer' usually means NPK, and that's probably what your dad is thinking of, but soil fertility requires more than these three atoms. To ensure that my soil starts with some NPK, I supplement my compost with organic fertilizer when I create a new garden bed. But the presence of Calcium, Magnesium, Iron and a host of other atoms are required for plant health. Compost makes those metals and minerals available to the plant by mediating the chemical reactions between the dirt and the plant, so in a manner of speaking compost is an indirect fertilizer.

Compost also creates the environment where the soil food web can exist. Entire books are written describing the soil food web so I won't attempt to describe its benefits here. But it's enough to say that the soil food web creates an optimal environment for plants.

Get your dad involved in discovering how to make the soil fertile. You'll both benefit from that.