Meine Schwester ist dafür, aber mein Bruder ist dagegen.

Because mein changes its ending to match the gender, number, and case of the noun.

In this sentence, both nouns are in the nominative case because they are the subjects:

• meine Schwester = my sister
• mein Bruder = my brother

For possessive words like mein:

• masculine nominative: mein Bruder
• feminine nominative: meine Schwester
• neuter nominative: mein Kind
• plural nominative: meine Freunde

So the -e in meine appears because Schwester is feminine.

In a normal German main clause, the finite verb usually comes in position 2.

So:

• Meine Schwester = position 1
• ist = position 2
• dafür = the rest of the clause

And in the second clause:

• mein Bruder = position 1
• ist = position 2
• dagegen = the rest

This is one of the most important word-order rules in German.

Here they mean:

• dafür sein = to be in favor of it / to support it
• dagegen sein = to be against it / to oppose it

These are very common expressions in German.

So:

• Meine Schwester ist dafür = My sister is in favor of it
• mein Bruder ist dagegen = My brother is against it

The da- part points back to something already mentioned or understood from context.

German often uses da-compounds like dafür, dagegen, darauf, damit, and so on to refer back to a thing, idea, action, or situation.

Instead of saying:

• für das
• gegen das

German usually prefers:

• dafür
• dagegen

This is especially common when referring to an idea such as:

• a plan
• a proposal
• a decision
• a suggestion

So if the topic is already known, dafür and dagegen sound natural.

Usually dafür is the more natural choice when you are referring back to something non-human that was mentioned before.

For example:

• Bist du für den Plan? = Are you in favor of the plan?
• Ja, ich bin dafür. = Yes, I’m in favor of it.

Using für das is much less common in this kind of sentence.

A useful rule:

• use da-compounds like dafür for things/ideas
• do not usually use them for people

So you would say:

• Ich bin für ihn. = I’m for him. not:
• Ich bin dafür if you mean for him

Because aber is joining two main clauses, and in German these are normally separated by a comma.

The two clauses are:

• Meine Schwester ist dafür
• aber mein Bruder ist dagegen

German punctuation is often stricter than English here. The comma before aber is standard.

Because after aber, you still have a normal main clause, and the verb still needs to be in second position.

So the correct order is:

• mein Bruder = first element
• ist = second position
• dagegen = later in the clause

Aber itself does not count as part of the clause structure in the same way that the first element does. It simply connects the two clauses.

Usually, no. In German, you normally repeat the verb in the second clause:

• Meine Schwester ist dafür, aber mein Bruder ist dagegen.

In English, we often omit repeated words:

• My sister is for it, but my brother against it
  That sounds incomplete in standard English too, and in German it is also incomplete.

German generally needs the full clause here.

Not exactly, though they are related.

• dafür sein = to be in favor of something
• zustimmen = to agree (with something/someone)

For example:

• Ich bin dafür. = I’m in favor of it.
• Ich stimme zu. = I agree.

Dafür sein focuses more on supporting an idea or proposal.
Zustimmen focuses more on agreeing.

Likewise:

• dagegen sein = to be against something
• ablehnen = to reject something

So the sentence sounds very natural for expressing opinion or stance.

Because mein/meine already functions like a determiner, so you do not normally add der/die/das as well.

You say:

• meine Schwester
• mein Bruder

not:

• die meine Schwester
• der mein Bruder

Possessive words like mein, dein, sein, ihr, unser, etc. usually take the place of the article.

Yes, but it sounds different.

• dafür / dagegen is the most neutral and everyday way to say it.
• pro / kontra exists, but it is more like pro / con in English and can sound more formal, abstract, or debate-like.

So for ordinary conversation, dafür and dagegen are usually the best choice.

You could stress aber, dafür, or dagegen in speech, depending on what you want to emphasize.

You could also slightly change the wording:

• Meine Schwester ist dafür, mein Bruder dagegen.

This is a shortened version and is also natural, especially in speech or writing where the omitted ist is understood from the first clause. But for learners, the full version:

• Meine Schwester ist dafür, aber mein Bruder ist dagegen.

is clearer and safer to use.