What is the Malthus' theoretical argument ?

The Original Malthus' theoretical argument: In 1798, Thomas Malthus proposed his theory in An Essay on the Principle of Population. He argued that although human populations tend to increase, the happiness of a nation requires a like increase in food production.

"The happiness of a country does not depend, absolutely, upon its poverty, or its riches, upon its youth, or its age, upon its being thinly, or fully inhabited, but upon the rapidity with which it is increasing, upon the degree in which the yearly increase of food approaches to the yearly increase of an unrestricted population."

However, the propensity for population increase also leads to a natural cycle of abundance and shortages:

  We will suppose the means of subsistence in any country is just equal to the easy support of its inhabitants. The constant effort towards population...increases the number of people before the means of subsistence are increased. The food, therefore, which before supported seven millions, must now be divided among seven million and a half or eight million. The poor consequently must live much worse, and many of them are reduced to severe distress. The number of labourers also being above the proportion of the work in the market, the price of labour must tend toward a decrease; while the price of provisions would at the same time tend to rise. The labourer therefore must work harder to earn the same as he did before. During this season of distress, the discouragements to marriage, and the difficulty of rearing a family are so great, that population is at a stand. In the meantime the cheapness of labour, the plenty of labourers, and the necessity of an increased industry amongst them encourage cultivators to employ more labour upon their land; to turn up fresh soil, and to manure and improve more completely what is already in tillage; till ultimately the means of subsistence become in the same proportion to the population as at the period from which we set out. The situation of the labourer being then again tolerably comfortable, the restraints to population are in some degree loosened; and the same retrograde and progressive movements with respect to happiness are repeated.

— Thomas Malthus, 1798. An Essay on the Principle of Population, Chapter II.

Famine seems to be the last, the most dreadful resource of nature. The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race. The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction and often finish the dreadful work themselves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague advance in terrific array, and sweep off their thousands and tens of thousands. Should success be still incomplete, gigantic inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world.

— Thomas Malthus, 1798. An Essay on the Principle of Population. Chapter VII, p. 61

Malthus faced opposition from economists both during his life and since. A vocal critic several decades later was Friedrich Engels.