This is uninformed speculation, but I imagine two reasons:

1. You can skim an aggregated list of headlines and get a quick glance of current events without ever clicking through to the actual sites, thus causing them to lose out on ad revenue.

2. Newspapers like being linked to but don't want their competitors linked to, and think they'd be better off overall in a world where people directly visited the web site of their preferred news outlet.

This is mainly done to prevent linking and hosting pirated material; think movies and music. Newspapers and blogs are just collateral damage.