Line Managers/ HR personnel are not your employer.
Escalate to good offices of appointing authority,MD,Chairman.
Such companies are covered by ( name of the state) Shops and commercial Establishments Act that was enacted to govern the service conditions of employees working in such establishments. Leave is also governed.
The employer can provide superior benefits but not inferior.
Leave policy of the company can be framed as per negotiated settlement between employer and representatives/union/trade unions of employees and as per standing orders.........
Many companies do have paternity leave.
Your query emphasizes that:
1. There is a need for the employees to unite and negotiate.
2. The employees should promote united families and while parents take care of working children, working children take care of aged parents.
3. Employers do not marry or adopt employees. Employees should not treat employer as married partner or parent and defend their interest. United employees can defend their interest much better than isolated (nuclear) employees.
You can obtain list of employee’s union (IT sector) from many other threads e.g.;
https://www.lawyersclubindia.com/forum/Employment-situation-116491.asp#.VODF-IKqqko
https://www.lawyersclubindia.com/forum/Us-visa-bonds-116550.asp#.VODCtIKqqko
Check the leave policy of the company and standing orders to find Paternity leave.