Why don't we teach our students more skills rather than pushing to complete a curriculum?

It is due to the prevailing examination system. Students, teachers and parents use their all efforts to secure more marks in the examination to grab good opportunities in further studies. This target can only be achieved by putting emphasis on curriculum. 

Although it is not a bad idea but even the top scorers need to develop certain skills to get in higher education later on.

Curriculum is an important component of teaching. It is a guideline of objectives of education. It is as guidance in order to keep on the track to obtain the objectives. So even an educational institution/ school want to teach skills more, they also will be required to make curriculum in which describe the materials/ necessity contents of the skills that will deliver to the students. Basically good curriculum have to accommodate skills on the curriculum, just the proportion are different in each institution/ school.

We should modify our curricula to accommodate more skill based outcomes, this is ensured by adding more project based learning and hands on activity. The skills and outcomes covered in such ways are the ones that are fully understood by the student.