Why might two elements possess similar chemical properties

One of the reasons can be because their atoms have the same outermost shell electrons.

For example in elements fluorine and Chlorine, they both have 7 outermost shell electrons. We can know this because they're in the same group in the periodic table, which is group VII. Both of these elements have similar chemical properties, such as they both react with sodium to produce metal halides, which is a kind of salt.

However, note that their chemical properties will not be exactly the same, as they have different number of protons which distinguishs between different elements.

That would be a working theory.