OK, you DFA Tavarez, and call up Hansen or Van Buren. Both pitchers have had trouble throwing strikes, and both get shelled upon returning to the bigs. Now, you've already gotten rid of Tavarez, and Hansen and Van Buren aren't ready, who do you go to?
You're left sifting through other team's garbage, all the while eating Tavarez's 6.2 million dollar salary.
Hansen needs more time at the AAA level. If Tavarez is still struggling come July 31st, there's a good chance he could be DFA'd, but it's only June 11th, and arguably his ERA could be lower if Francona didn't leave him out too long on several occasions. Also, this guy has been a serviceable reliever for the last three years, you want to DFA him because he had a bad stretch? Give him some time to work out his troubles, he'll be able to go back into his previous spot in the bullpen when Timlin arrives.