Мне пришлось долго объяснять свою позицию, чтобы убедить коллегу перенести встречу.

Because the expression мне пришлось literally works like it fell to me / I had to.

In Russian, прийтись / приходиться is often used in an impersonal construction:

• мне пришлось = I had to
• ему пришлось = he had to
• нам пришлось = we had to

So мне is in the dative case, not the nominative, because it marks the person affected by the necessity.

Пришлось is the past tense of прийтись and here means had to or was forced to.

It often suggests that the speaker did something because the situation required it, not because they wanted to. So compared with a plain English had to, it can sound a little more like:

• I ended up having to...
• I was obliged by circumstances to...

In this sentence, Мне пришлось долго объяснять... means the speaker had no easy alternative.

Both can sometimes translate as I had to, but they are not the same.

• мне пришлось = necessity caused by circumstances
• я должен был = obligation, duty, expectation, or personal responsibility

Compare:

• Мне пришлось долго ждать.
  = I had to wait a long time.
  The situation forced this.

• Я должен был подождать.
  = I was supposed to wait / I was obliged to wait.
  This sounds more like duty or instruction.

In your sentence, мне пришлось is very natural because the speaker is describing a situation they were forced to deal with.

After пришлось, Russian normally uses an infinitive to say what someone had to do.

So the pattern is:

• мне пришлось + infinitive

Examples:

• Мне пришлось уйти. = I had to leave.
• Ей пришлось работать. = She had to work.
• Нам пришлось объяснять. = We had to explain.

So объяснять is there because it names the action that became necessary.

This is an aspect question.

• объяснять = imperfective
• объяснить = perfective

Here объяснять is used because the sentence emphasizes the process and duration: долго объяснять = to explain for a long time.

If you said Мне пришлось объяснить свою позицию, it would focus more on the completed fact of giving the explanation. But with долго, Russian strongly favors the imperfective because the action is presented as extended.

So:

• долго объяснять = spend a long time explaining
• объяснить would sound less natural with that process emphasis

Свою позицию is in the accusative case because it is the direct object of объяснять.

Base form:

• своя позиция

In this sentence:

• свою позицию = one's position / one's stance

The verb объяснять takes a direct object:

• объяснять что?
  позицию

So the noun changes to accusative:

• позиция → позицию

And the adjective/pronoun changes to match:

• своя → свою

Свой is the reflexive possessive pronoun, meaning one’s own. Russian often uses it instead of мой / твой / его when the possessor is the same as the subject of the action.

Here, the speaker is the one explaining the position, so:

• объяснять свою позицию = explain one’s own position

Using мою позицию is not impossible, but свою is usually more natural in this kind of sentence.

A useful rule:

• if the owner is the same person as the subject, Russian often prefers свой

Examples:

• Я люблю свою работу. = I love my job.
• Она открыла свою сумку. = She opened her bag.

Чтобы introduces a purpose clause. Here it means in order to or so that.

So:

• Мне пришлось долго объяснять свою позицию, чтобы убедить коллегу...
• I had to explain my position for a long time in order to convince my colleague...

It connects the first action with its goal:

• first: explaining
• goal: convincing the colleague

After чтобы, Russian can use either:

• a past-tense verb form
• or an infinitive

The infinitive is common when the subject is understood in a general or same-subject sense, especially in purpose constructions.

Here, чтобы убедить коллегу means:

• in order to convince the colleague

The person doing the convincing is the same speaker who was explaining, so the infinitive is very natural.

Compare:

• Я пришёл, чтобы поговорить.
  = I came to talk.

• Я написал ему, чтобы он пришёл.
  = I wrote to him so that he would come.

In the second example, он is a different subject, so a finite verb is used.

Коллегу is in the accusative case because it is the direct object of убедить.

Pattern:

• убедить кого? в чём?
• to convince whom? of what?

In your sentence, only the person is stated directly:

• убедить коллегу = convince the colleague

If you wanted, you could also add what you convinced them of:

• убедить коллегу в необходимости перенести встречу
• convince the colleague of the need to move the meeting

Because убедить points toward a result: the goal is to get the colleague to agree to one completed action, namely moving/rescheduling the meeting.

• перенести = perfective, one completed action
• переносить = imperfective, process or repeated action

Here the meaning is:

• to convince the colleague to reschedule the meeting

That is a single completed act, so перенести is the natural choice.

Because each verb is showing a different kind of action.

• объяснять = imperfective
  Focus on the ongoing process: the speaker spent a long time explaining.

• убедить = perfective
  Focus on the intended result: to convince the colleague.

• перенести = perfective
  Focus on the completed action the colleague would take: reschedule the meeting.

So the aspects are chosen very logically:

1. долго объяснять → process over time
2. убедить → achieve a result
3. перенести → complete one specific action

No, Russian word order is flexible, though the given order is very natural.

Current order:

• Мне пришлось долго объяснять свою позицию, чтобы убедить коллегу перенести встречу.

This sounds neutral and clear:

1. necessity
2. action
3. purpose
4. result

You could rearrange parts for emphasis, for example:

• Чтобы убедить коллегу перенести встречу, мне пришлось долго объяснять свою позицию.

This puts the purpose first:

• In order to convince my colleague to reschedule the meeting, I had to explain my position for a long time.

So the word order can change, but the original version is a very standard neutral sentence.

It most often means reschedule or move to another time.

Depending on context, English might translate it as:

• move the meeting
• reschedule the meeting
• sometimes postpone the meeting

But перенести does not automatically mean only later. It can mean moving the meeting to a different time in general. If Russian specifically wants to stress postpone to a later time, context usually makes that clear.

So перенести встречу is best understood as:

• to reschedule the meeting

The sentence is already natural, but Russian offers close alternatives depending on style.

For example:

• Мне пришлось долго объяснять свою позицию, чтобы убедить коллегу перенести нашу встречу.
  Adds our meeting.

• Мне пришлось долго объяснять, почему я так считаю, чтобы убедить коллегу перенести встречу.
  More conversational: I had to explain for a long time why I thought so...

• Я долго объяснял свою позицию, чтобы убедить коллегу перенести встречу.
  This removes the nuance of forced necessity and just states the action.

So the original sentence is good, especially if you want to keep the idea of I had to.