Apart from the obvious moral issue, there's also the fact that you risk encouraging other types of discriminatory behavior against all females, because after all, if this particular type of discrimination is acceptable, then why should this other type of discrimination not be?
You may argue that a female fetus is not comparable to a female who has already been born, but that's an opinion, not a fact, and people will disagree with you.
You also risk alienating your female population, making them feel unwanted or inferior, which can have numerous effects on their self-worth and quality of life.
politics.stackexchange.com/users/16903/Jaood
In addition to the other answers, there is a social and economical problem, at least in China: Eastern Asian countries (China, South Korea, Japan,...) are very conservative and are the family organization is tightly structured:
You get a good job.
You get married.
You make children.
You spend money on the education of your children so that they enter a good university.
Your children graduate the university and get a good job.
Your children take care of you when you get older.
The importance of the family and solidarity between generations is especially important since the welfare system in these countries is not as developed as it can be in Western countries.
A lack of women means that many men will stay unmarried, and be without children to take care of them.
Also, culturally, being unmarried is seen as a big failure in life.
politics.stackexchange.com/users/4494/Taladris
Wouldn't it also mean there is a large number of men with no woman to marry?
That may lead to higher rates of sexual deviance, as a large number of single men are sleeping around with other people's wives, leading to higher divorce rates, adultery, and the possibility of rape.
It could also lead to an emigration of men who can't find wives which would impact the work force of a country that is trying to industrialise itself.
The government would have an interest in preventing adultery and promiscuity for the purposes of preventing STI's, and also preventing divorces.
They also have an interest in keeping a strong workforce so keeping working age men from emigrating is important.
Also, as suggested in the comments, China has a big problem with women from other countries being imported as sex slaves for lonely men due to the lack of women to marry, this is also obviously problematic and costs the government money.
http://thediplomat.com/2017/07/chinas-trafficked-brides/
politics.stackexchange.com/users/14439/Charlie
When one group with some common concerns is targeted for abortions, their powers in democracy are diminished.
An sample to illustrate easier: blacks in the USA.
About twenty million blacks fetuses have been aborted in the USA since Roe v Wade.
The current Black population is forty million.
How much more powerful of a voting block would sixty million be?
They'd get more politicians that appealed to them and cared about their struggles.
The last election result would have flipped unless the rhetoric used was different.
Now apply the above to women.
Can having a bias in the voting population bias against women negatively affect them?
Yes.
politics.stackexchange.com/users/10482/Lan
It is the moral issue.
You seem to think that any policy can be analysed in terms of (economic) benefit to the government.
You ask "why is it in the government's interest".
My case is that governments often don't act in their own economic interest.
Governments are not just machines generating profit.
They are composed of people who started doing their job because they thought that they could make their country a better place for the people living in it (better and not just richer).
Politicians are moral creatures.
The Law of the Land is a written expression of the moral choices made by politicians over the years.
In all countries, the political leaders can act to prevent something just because it is wrong .
As an example, consider the UK Hunting Act (2004) which bans the hunting of wild mammals (eg foxes) with dogs.
There is very little economic case for banning fox hunting.
The foxes can't vote.
The reason for the ban was moral .
A majority in Parliament believed that hunting with dogs was wrong .
Many countries have anti discrimination laws.
In India, discrimination by caste is illegal.
The reason is not the economic interest of the government, it is moral.
The law in China is weaker (as might be expected from a totalitarian government), but Chinese employment law disallows discrimination by gender.
The reason for this law is again because the Chinese government want to disallow actions that they see as wrong.
There does not need to be an economic argument for such a law, (and the Chinese government doesn't need to worry about votes.)
The fact that something is wrong is sufficient reason to legislate Now creating a gender imbalance in society may have some negative impact, which would add to the other social issues that India and China face.
But this is not the reason that it is "a very large issue".
Instead, the political leaders see sex-selective abortion as a moral failure and so create policies to act against it.
politics.stackexchange.com/users/8554/James K
India is a constitutional democracy and it is in the best interest of the Government to "defend the Constitution".
The Indian Constitution (and thus the people of India) enshrines the value of equality and non-discrimination on the basis of gender.
Also, sex-selective abortion is morally as well as legally considered to be discriminatory against the female sex, and it also could further justify other subtle forms of gender discrimination.
Even the policy of population control, however urgent, needs to be within the bounds of the law of the land.
Thus, the Government cares a lot to prevent sex-selective abortion.
politics.stackexchange.com/users/12440/SMJoe
What's wrong with sex-selective abortions?
Done in volume, as it was in China and India, you will end up with an entire generation that has an imbalance, as in a lot more men than women.
So, what happens when that generation reaches childbearing age as is currently the case?
Not enough women...
lower birth rate that can't be quickly corrected.
That can ripple through several generations.
politics.stackexchange.com/users/14788/tj1000
It is often claimed that China and India have tens of millions of women "missing" because of sex selective abortions and that apparently this is a "very large issue". But why exactly would it be a big problem from the government's point of view?  Both China and India are trying to control the fertility rate and obviously having less women means you will have less children. So is it simply a moral issue of aborting fetuses because they're female?
Why would the government care about sex-selective abortions?
politics.stackexchange.com
<india><china><abortion>
politics.stackexchange.com/questions/23811
politics.stackexchange.com/users/7434/JonathanReez
Apart from the obvious moral issue, there's also the fact that you risk encouraging other types of discriminatory behaviour against all females. If this particular type of discrimination is acceptable, then why should any other type of discrimination not be? You may argue that a female foetus is not comparable to a female who has already been born, but people  will  disagree with you.   The government would care because it is wrong from a moral perspective and will encourage discriminatory behaviour towards women. 
The government would care because it is wrong from a moral perspective and will encourage discriminatory behaviour towards women. 