Why is it considered bad practice to lock non-static fields?

And, if I am not locking non-static fields, then how do I lock an instance method without locking the method on all other instances of the same or derived class?

I wrote an example to make my question more clear.

public abstract class BaseClass
{

    private readonly object NonStaticLockObject = new object();
    private static readonly object StaticLockObject = new object();

    protected void DoThreadSafeAction<T>(Action<T> action)
        where T: BaseClass
    {
        var derived = this as T;
        if(derived == null)
        {
            throw new Exception();
        }
        lock(NonStaticLockObject)
        {
            action(derived);
        }
    }
}
public class DerivedClass :BaseClass
{
    private readonly Queue<object> _queue;
    public void Enqueue(object obj)
    {
        DoThreadSafeAction<DerivedClass>(x=>x._queue.Enqueue(obj));
    }
}

If I make the lock on the StaticLockObject, then the DoThreadSafeAction method will be locked for all instances of all classes that derive from BaseClass and that is not what I want. I want to make sure that no other threads can call a method on a particular instance of an object while it is locked.