Isn't this rather how humans build up immunities to things such as venoms? By giving someone very, very small doses of snake venom, they will eventually become immune to it? I guess it's true, even the most illogical of things come from logical backgrounds
At a very high level, yes, homeopathy and vaccination are similar... in that they both involve receiving a dose of something bad for you that's been neutralised somehow so it's no longer bad for you, to cure a similar bad thing. There are, however, plenty of differences:
Firstly, vaccination focuses on what's causing the disease whereas homeopathy focuses on symptoms... eg a flu vaccination helps immunise you against that strain of the flu, and won't help with other things that cause coughing, a blocked nose and a fever... or even other strains of the flu that aren't in that particular shot... but in homeopathy, since, say, arsenic poisoning causes many symptoms, including headaches, diarrhoea and vomiting, homeopathic arsenic is used to treat symptoms including headaches, diarrhoea and vomiting (without worrying about what's actually causing those symptoms). Back in the real world, becoming immune to arsenic, even if that were possible, isn't going to help you fight other problems that have similar symptoms to arsenic.
Secondly, vaccination makes it so that the dose, while based on something bad for you, is actually harmless, by tampering with the viruses in the dose so that they're inert... not able to actually function... but similar enough that the antibodies you get by fighting this inactive virus are also functional at fighting the real thing. Thus, it gets rid of the bad parts and leaves the good parts. Homeopathy makes it so that the dose, while based on something bad for you, is actually harmless, by diluting it so much that there isn't any of it left. Thus, it gets rid of the bad parts and gets rid of the good parts, and gets rid of the all trace of anything resembling the original ingredient.
Thirdly, vaccination focuses on things you can actually become immune to, like viruses... it's like how, once you get chicken pox as a kid, you'll never get it again - once you've gotten it once, your body reacts and you're now immune. A chicken pox vaccine simply triggers the same response so you become immune, without the hassle of actually catching the disease in the first place (thus, as I said in the previous point, getting rid of the bad parts and leaving the good parts). Homeopathy, on the other hand, doesn't seem to... you're not going to become immune to arsenic, no matter how much of it your body is exposed to, even if you could
find a way to safely expose yourself to it (a homeopathic solution doesn't count as "safe exposure" because, while safe, it doesn't count as "exposure").
Fourthly, vaccination is used solely as a preventative... giving a flu shot to someone who already has the flu isn't going to cure them... but giving it to someone who hasn't gotten the flu yet will help stop them from getting it. Homeopathy on the other hand, while it might be used as a preventative (I'm not certain either way) is also often used as a cure.
Finally, and most importantly: Science says that vaccination actually works. Science says that homeopathy doesn't work.