Tukukkk

My sensi says while sparring you should express your inner tiger. My understanding is that I should be savage and angry. But I don't like being angry! Is it possible to be good at sparring without anger impulses?

What works for your sensei might not work from you. He is teaching you, what had worked for him. For some, they use anger for the aggressiveness it brings. Anger dominates certain opponents. And in the case of draw, the more aggressive fighter that attacks more (whether contact or not) is usually declared the winner.

But anger does not work for everyone. It results in your judgment being clouded, tunnel vision, rash decisions leading to mistakes, disqualifications due to fouls, not to mention raising your blood pressure and heart rate for the wrong reasons.

I prefer teaching students to fight with a cool head, but maintaining an 'afraid-to-lose' mentality. As in, never let the other guy score more points than you. And reactive fighting. Seeing an opening results in automatic launching of a kick to that area.

Emotions in general are detrimental to your sparring.

Usually when I have seen this said to a student it is not because we want you to get angry, but that you are sparring as if you are afraid. If you are afraid of striking your opponent you become SLOW and hesitant. Remember here that you should only ever spar willingly (never spar if you don't want to) and also that your partner is in the same position.
Hitting your partner (or at least trying in earnest to do so) is actually beneficial to them, if you don't hit them (by reacting calmly to the openings they present) then they will have a false sense of security/confidence going into other bouts and wind up getting hit more.

Sparring 'Angry' is usually an attempt by your opponent to intimidate you into losing confidence and not trying hard. Many people will try this tactic, learn to deal with it and keep your calm as they are using that instead of skill to try to win. Once you have dealt with people sparring this way a couple of times you will learn to cherish new opponents that try it as they are easy to pick apart and usually don't have any other tactic to fall back on.

As @Kristina Lex says - reacting to the situation and putting a hand or foot to any target that presents itself is key - and much easier if you aren't angry/afraid/flustered - leave emotions at the door of the Dojang or on the pads/bags