Why does dropping foreign keys in sql server take long?

Dropping a constraint requires an Sch-M (Schema Modification) lock that will block others to query the table during the modification. You are probably waiting to get that lock and have to wait until all currently running queries against that table are finished. A running query has an Sch-S (Schema Stability) lock on the table and that lock is incompatible with an Sch-M lock. From Lock Modes, Schema Locks

The Database Engine uses schema modification (Sch-M) locks during a table data definition language (DDL) operation, such as adding a column or dropping a table. During the time that it is held, the Sch-M lock prevents concurrent access to the table. This means the Sch-M lock blocks all outside operations until the lock is released.Some data manipulation language (DML) operations, such as table truncation, use Sch-M locks to prevent access to affected tables by concurrent operations. The Database Engine uses schema stability (Sch-S) locks when compiling and executing queries. Sch-S locks do not block any transactional locks,

including exclusive (X) locks. Therefore, other transactions, including those with X locks on a table, continue to run while a query is being compiled. However, concurrent DDL operations, and concurrent DML operations that acquire Sch-M locks, cannot be performed on the table.

• Steps to drop a foreign key SQL server
• In Object Explorer, expand the table with the constraint and then expand Keys. Right-click the constraint and then click Delete. In the Delete Object dialog box, click OK.