Why do we give sympathy to women?

This is a leftover traditional female privilege.  Historically (traditionally), women were protected and provided for by men and the society.  The feminists at the turn of the century deemed the traditional arrangements to be "oppressive" to women and demanded equal Rights instead instead of the privilege system.

That happened long ago, well before we were all born.  But what hasn't happened is the dropping of female privileges from under the traditional system, in order to properly migrate into equality.  So women in the West today have equal Rights, without equal Responsibilities.  All the modern Rights and privileges without the corresponding Responsibilities and obligations.  It's the best of both the modern system and the traditional system for women.  Of course this is highly unfair for men, and not anything that looks like equality.

Prominent feminists work their hardest to keep this privileged condition by claiming the we "still aren't there yet" with regards to gender equality, even though they have full agency and equality of Rights to men.  The feminist idea of "gender equality" now is to entirely rework society into something radically different that what we have today, without allowing any discussion about it.

Good question Damiana. I will find you. And I will tell you the answer. God's answer. WHEn god made man, the woman was the one who gave him the apple you see.... the evil apple. That is why, women are temptresses and evil ones at that. I can assure you that you are being seduced into the intoxicative miasma of the sorcress. Do not sympathize with women.... EVER

I think you're meaning a bit vague. There is a view to regard women as a weak group in history. They got suffrage not far ago. Both in physique and mental fields, they have disadvantages. They suffer from periods, pregnancies, cultivating children.

They need to make up to keep attraction and their floriated youth is fragile and short. The traditional culture is prone to respect and take care of them more preferentially. It's fair and right.

All this base on average view. Individually, a female might much more strong than the average male mentally and physically.

It's good to give women sympathy as far as they still naturally reproduce humans.

Why should women have to think about our own safety in this way, all the time, every day, and not be able to do things which are everyday for men to do, and to watch carefully everything we say and do so as not to give people an "excuse" to harrass and assault us?

Why do we give sympathy to anyone? Because we do when we have a heart. 

Sympathy is not limited to gender, we extend sympathy to people who are victims.

Why do we give sympathy to rich people whose houses are burglarized? I mean why didn't those rich people think before displaying their wealth with a mansion?

Why do we give sympathy to people that get hurt in car crashes? Everyone knows that cars can be dangerous, right?

Why do we give sympathy to a man that gets assaulted when walking home through a bad neighborhood? Shouldn't he have found a different route to walk?

Why do we give sympathy to the gas station attendant who got held up at gunpoint and robbed at night? After all, he knew it was a job that posed potential risks, yet he took it anyway.

The reason humans sympathize with other humans is because of basic compassion, empathy, and good heartedness. 

Women have always been given sympathy.

Men give them homes to live in. Cars to drive. Roads to drive the cars on. Technology. The Internet and cell phones. Food and medicine. 

All provided for by men. 

Women should be very thankful. 

Because all women are oppressed by men who are all part of the patriarchy.  

We owe sympathy to those suffering when we have so suffered.  We owe empathy to anyone suffering, that is to imagine ourselves in the same situation and what needs we might incur, so that we can help as we are able.  Neither sympathy nor empathy need take into account fault or cause, and certainly not gender.  Which should be obvious to anyone, begging the question:  Is this a question or just a misogynist ran in the form of a question?