Why did Malthus thought that population increases geometrically while resources increase arithmetically?
As mentioned in the question the exponential population growth was argued to exist because it is based on the 'natural growth' that can be empirically observed anywhere in nature where the resources are abundant. So you already answered that part pretty much yourself.
When it comes to the arithmetic growth of resources, the word resource is actually not appropriate modern economist would call things like food and shelter output not a resources which are factors of production (the wikipedia in this article uses the word resources improperly see Samuelson &amp; Nordhaus Economics). Resources are inputs not outputs of production.
The reason why Malthus thought that output/production would grow arithmetically is due to diminishing marginal product of factor of production. Diminishing marginal product means that although output increases when you use more factors (resources like land, labor, capital) the output increases at a diminishing rate. The diminishing returns as argued by many economist must apply otherwise even single plot of land could produce enough crops to feed whole world. At some point just throwing more labor and capital at a plot of land will simply lead to smaller output.
Malthus thus reasoned that due to these diminishing returns output will over time grow only arithmetically as given the fact that amount of land is fixed in the world at some point no matter how much machinery and labor force you apply to it at some point the output will increase only minimally (e.g. having 3 tractors for one acre field might increase output significantly compared to having 1 but having 100 tractors as opposed to 97 will not make much difference).
However, Malthus turned out to be wrong because he did not taken into account the effect of technology on production. A Malthusian production function would look something like:
$$Q=K^{0.3}L^{0.2}$$
which exhibits diminishing returns to scale as more and more inputs of labor and capital (resources) are put in the output will always increase but at diminishing rate (in fact if you would plot this curve you would see that as factor inputs increase the output increase becomes more and more ‘flat’ and ‘linear-like’ e.g. imagine a plot of square root function).
However, modern economists realize that technology plays a role in production process too. A modern production function would look like:
$$Q=AK^{0.3}L^{0.2}$$
where $A$ would be the level of avaiable technology. So as long as technology keeps accumulating and growing sufficiently fast enough to keep output with population growth Malthusian trap will not occur.