geureonde jageun somuneun geumbang peojinikka hamburo malhamyeon an dwae.

그런데 often means but, by the way, or however, depending on context.

In this sentence, it works like a soft transition:
But / the thing is, small rumors spread quickly, so you shouldn’t speak carelessly.

It does not strongly contradict the previous sentence; it often just introduces a new point or a caution.

Here, 작은 modifies 소문.

• 작다 = to be small
• 작은 = small, in front of a noun
• 소문 = rumor

So 작은 소문 means a small rumor or a minor rumor.

The reason it is 소문은 in the full sentence is because the noun is followed by the topic particle 은:

• 작은 소문은 = as for a small rumor / small rumors

So 작은 is just the adjective form, and 은 is the topic marker attached to 소문.

In Korean, descriptive verbs change form when they directly describe a noun.

• 작다 = to be small
• 작은 = small + noun

So:

• 작은 소문 = a small rumor
• 작은 집 = a small house

This is the normal noun-modifying form for 작다.

The particle 은 marks 소문 as the topic of the sentence.

So 작은 소문은 금방 퍼지니까... gives the sense of:

• As for small rumors, they spread quickly...
• Small rumors spread quickly, so...

Using 은 often gives a general or contrastive feeling. It can imply something like:

• when it comes to small rumors,
• small rumors, you know, spread quickly

It is not just identifying the subject; it is setting the topic.

금방 means quickly, soon, or in no time.

In this sentence:

• 금방 퍼지다 = spread quickly

So 작은 소문은 금방 퍼지니까 means
because small rumors spread quickly.

A useful nuance: 금방 often suggests that something happens sooner than you might expect.

퍼지니까 comes from:

• 퍼지다 = to spread
• -니까 = because / since

So 퍼지니까 means because it spreads or since it spreads.

In this sentence:

• 작은 소문은 금방 퍼지니까
  = because small rumors spread quickly

The ending -니까 gives a reason for the warning in the second part:

• 함부로 말하면 안 돼
  = you shouldn’t speak carelessly

So the overall logic is:

Because small rumors spread quickly, you shouldn’t speak carelessly.

Because Korean uses 퍼지다 very naturally for things like rumors, news, smells, or influence spreading outward.

• 소문이 퍼지다 = a rumor spreads
• 냄새가 퍼지다 = a smell spreads
• 소식이 퍼지다 = news spreads

So this is a very natural verb choice here.

함부로 means something like:

• carelessly
• recklessly
• without thinking
• without proper caution
• sometimes arbitrarily

In this sentence, it means speaking too freely or irresponsibly.

So:

• 함부로 말하다 = to speak carelessly / to say things recklessly

It has a warning tone: not just casual speech, but speech that could cause problems.

This is the pattern:

• Verb stem + -(으)면 안 되다

It means:

• must not
• should not
• it is not okay to...

Here:

• 말하다 = to speak / say
• 말하면 = if you speak / if you say
• 안 돼 = it must not be / it is not allowed

Together:

• 말하면 안 돼 = you shouldn’t say that / you must not speak that way

Very literally, it is closer to If you speak, it is not okay, but in natural English it means You shouldn’t speak carelessly.

Yes, in natural translation it is usually understood as you, but Korean often leaves subjects unstated when they are obvious from context.

So:

• 함부로 말하면 안 돼
  literally = If speak carelessly, it’s not okay
• natural English = You shouldn’t speak carelessly

Depending on context, it could also mean:

• one shouldn’t speak carelessly
• people shouldn’t speak carelessly

But in everyday conversation, it most often feels like the speaker is warning the listener.

It can feel more natural in English as:

• even a small rumor
• a minor rumor
• the slightest rumor

The Korean phrase is literally small rumor, but the idea is that even something that seems insignificant can spread quickly.

So the nuance is not really about physical size, of course. It means the rumor may seem minor or trivial, but it can still spread fast.

안 돼 is a casual, informal style.

Compare:

• 안 돼 = casual
• 안 돼요 = polite
• 안 됩니다 = formal

So this sentence sounds like something said in everyday conversation to a friend, younger person, family member, or someone the speaker is speaking casually with.

The meaning stays basically the same, but the tone changes with speech level.

Yes, in many situations you could say something like:

• 작은 소문은 금방 퍼져서 함부로 말하면 안 돼

But -니까 is often especially natural when giving a reason for advice, commands, or warnings.

So:

• 퍼지니까 = because it spreads, so...
• this fits very well with a caution like 안 돼

That is why -니까 sounds very appropriate here.