A friend asked today," what to reply someone who asks that Shri Ram was so mysogynist that he disregarded his wife just to save himself from slurs of few people?"

Let's look into this claim in brief from reference of Valmiki Ramayana.

First thing, in Valmiki Ramayana it is clearly specified that Shri Ram knew that Maa Sita was pregnant.
They were talking in garden one evening.
Shri Ram had asked that now you are going to be mother.
You have to take extra care of yourself.

What should I do to make you happier?

Maa replied that Since we returned from Vanvas, I haven't got much time to serve the Sages and go to Ashram of Sages.

If you think it's possible I would like to visit some Ashram and reside there for some period.

We are still advised today to hear Satsang, read scriptures and do Punya karma when in pregnancy so that our children are inculcated with Good Sanskar even before they're born.

Shri Ram had promised her that he'll order Laxman or Bharat to take her to some Ashram.

Now let's look at second instance.
Shri Ram knew that How important it is for a king and queen to maintain a dignity.

He is the one who leads his people.

He has to set an example.

Even in recent times, we see an example of such dignity when Lal Bahadur Shastri ji resigned from Railway Minister post just after a railway incident even though he was not responsible for it.

When Shri Ram heard that people are maligning Sita and then using her case to justify other cases, he had to take some action not as a husband but as a king. He was a king of Ikshvaku dynasty and known as Maryada Purushottam.

If people would start misquoting his actions then how could he set an example of a righteous king for the next generations?

He called Laxman, Bharat and Shatrughn and informed them about the incident.

He didn't just asked Laxman to leave her anywhere.

He specifically tells that Laxman should leave Sita near Ashram of Sage Valmiki. It was also what Maa Sita wanted and she could live dignified life there.

Now, I want to ask such fellow people who dare to question Sita and Ram:
1. Do you consider Ramayana to be a history and not mythology?

2. While comparing Shri Ram and Sita from today's situation, Are you interacting with Deities and Rakshasas in the way they interacted?

3. Can you take millions of Vanaras and an old Vulture to fight alongside you and even die to save you?

4. Can you follow your husband to extremities when he has lost everything he had in life and is going to live like a monk for next 14 years?

5. If you know that your wife is in the clutches of a barbarian who is known to be non human and has defeated even deities in battles, has killed even your ancestors, would you still go out to fight him if not a single person except your brother is there to stand with you?

6. Can you leave all your properties for 14 years just because your father can die with dignity and no one can question that he didn't kept his promises?

No. You can't.

So don't dare to question my God Shri Ram and My mother Maa Sita.

They are not just human to be compared with.

Follow her. Read her from primary sources of you can.
Jai Shri Ram.

Jai Maa Janak Nandini.