against it / however
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against it
Expresses an objection, a rejection, or an opposing position toward a previously mentioned matter or opinion.
Der Vorschlag klingt gut, aber ich habe trotzdem etwas dagegen.
The proposal sounds good, but I still have something against it.
however
Creates a contrast or comparison; means something like 'in contrast' or 'on the other hand'.
Mein Bruder liebt den Winter, ich dagegen bevorzuge den Sommer.
My brother loves winter; I, however, prefer summer.
for that
Refers to a measure that serves as a remedy or protection against a problem, danger, or illness.
Ich habe starke Kopfschmerzen, hast du etwas dagegen?
I have a bad headache; do you have something for that?
'Dagegen' is a pronominal adverb and is made up of 'da' and the preposition 'gegen'. It literally means 'against that' and refers to a previously mentioned thing or idea.
Ein neues Einkaufszentrum soll gebaut werden, aber viele Bürger sind dagegen.
A new shopping center is supposed to be built, but many citizens are against it.
The meaning depends heavily on the context. If 'dagegen' refers to an opinion, it expresses objection. If it compares two sentences, it means 'in contrast'. In a medical context, it asks about a remedy.
Ich bin für den Plan, mein Kollege ist aber dagegen.
I am in favor of the plan, but my colleague is against it.
When 'dagegen' expresses a contrast, it can stand in position 1, followed by the verb. But it can also stand after the verb and the subject in order to emphasize the subject.
Er liebt laute Musik. Dagegen bevorzuge ich die Stille.
He loves loud music. I, however, prefer silence.
for it / in favor
Dafür and dagegen can both refer to a remedy for a problem. Dafür emphasizes the purpose of the remedy, while dagegen marks the problem as something to be fought or alleviated.
Bei starken Kopfschmerzen gibt es ein Mittel, das dagegen helfen kann.
For severe headaches, there is a remedy that can help against them.
Bei starken Kopfschmerzen gibt es ein Mittel, das dafür gut geeignet ist.
For severe headaches, there is a remedy that is well suited for that purpose.
