Why travel to a new country to volunteer, I think the better question is why not? There are so many incredible opportunities that accompany the experience of traveling to a new country to volunteer: the opportunity to meet am amazing, new people who can become lifelong friends, the opportunity to learn about a new culture firsthand in a way that vacation type traveling cannot really provide, the opportunity to make a difference in the lives of local people and/or animals, the opportunity to realize that you are probably going to learn more from them, than they are from you (in the best way possible), the opportunity to push yourself far past your comfort zone in ways that you never imagined you would, the opportunity to experience tremendous personal growth, the opportunity to create memories you will cherish forever, the opportunity to see how incredibly different and yet, similar various cultures and countries are to your own, the opportunity to never see the world or life the same as before, and the opportunity to see how the world can be so incredibly small and gloriously vast at the exact same moment.
There is no limit to the type of opportunities that can present themselves when one travels to another country, not to vacation but to do meaningful volunteer work that truly helps and does more good than harm. Opportunities that can completely change your life and spark a passion in your heart that you never knew existed.
When you travel to a new country to volunteer, you are changed when you return home, whether you notice it immediately or not and whether it is only some little changes that have occurred or some massive ones; it is extremely hard to travel abroad and volunteer and not be positively impacted.
When you travel to a new country to volunteer you can become very vulnerable and can be faced with difficult obstacles that you had not really realized you were signing up for when you decided to embark on that adventure; language barriers, being pushed far outside of your comfort zone, sickness/ illness, confusion of being in the midst of a completely foreign culture and country, homesickness, etc.
However, these same obstacles that can make you feel vulnerable and intimidated can also cause you to realize how strong and capable you really are and force you to look at yourself and your life through a different light. Volunteering abroad also can shine a light on a new purpose in your life that you had not previously considered, or it can renew your faith in a purpose that you have previously believed you had. It also educates you far better than books or a lecture in a classroom can, because you are forced to face your own prejudices and ignorance and take a good look at them and see that really, as humans, we are all far more similar in the important things than we realize and that our little differences are much more useful the celebrated, rather than used to divide us; our laughter, tears and smiles all happen in the same language and that is all that really matters.
So again, why travel to another country to volunteer? Why not?