Object has "against" in it, that's the ob- part. The other part is "throw". The German comes from the Latin. (Why did they go for -stand instead of a word for throw?)
Once you get into learning German, it’s surprising how many compound words like this are actually direct translations of the Latin or Greek roots of the same English words. Hydrogen = Wasserstoff (water material); television = Fernseher (distance seer) and so on. It’s almost as if they had their own uncleftish beholding moment.
Your examples are relatively modern, but there is a huge number of compound German words that are calques of French words, Latin words or Greek words, and which have been coined several centuries ago.
For instance: circumstance => Umstand, or depend => abhängen, or expression => Ausdruck, or participate => teilnehmen.
German looks unfamiliar for English speakers mostly because all the words that English has borrowed as such from French or from classical languages have been translated into compound German words.
-stand is what is (to something) or what has been established (about something). E.g., Bestand – the totality of what has been established about something, or what is available, etc. So Gegenstand is what has been established as real-world (or in extension also abstract) resistance to our objectives (so that we have to deal with it) – or, as gegen- is also vis-a-vis, what we are facing.
The Latin objectum has a directional vector (figuratively, it's thrown at us), while Gegenstand is much more inert. It's like a world view of active exploration versus a tableau of the world around us.
German is a Germanic language. More specifically, it belongs to the West Germanic language family, which includes German, Dutch, English, Frisian, and Afrikaans.
Latin itself belongs to the Indo-European language family.
I think that because they have almost the same geographical origin and cultural overlaps, they share many words.
They're far enough apart that the words they share by common descent (cognates) are often hard to recognize. For example, Latin /k/ is often German /h/ (canis/Hund, centum/hundert, cordis/Herz, cornus/Horn). Philologists actually had to discover some of these laws in order to recognize the existence of the Indo-European (Germans say "Indo-Germanic") family that German and Latin are both a part of.
The directly-recognizable ones are usually "learned borrowings", because Germans have been very enthusiastic about learning Latin as scholars for a long time, and often consciously chosen to use Latin (or Greek) words.
