This seems to be related to this question, and my answer is basically the same:
You want him to go into the wood, but he hesitates? Great, that is natural and very nicely illustrates the concept of the "Threshold Guardian". Threshold Guardians generally try to prevent any kind of transformation. They are the inertia, the fear of the unknown, the indifference that keep the hero from comitting to his journey. In order to be successful (and, in the Greek sense, to evolve into a hero), the main character must defeat the Threshold Guardian. It is his first trial - the one that shows that he is worthy to participate in the journey that lies ahead and worthy, too, of the sympathy of the readers.
However, to defeat the Threshold Guardian, the main character must undergo the first minor transformation. In your case, he must get rid of his fear. As I have argued in the answer to the question above, transformation is neither pleasant nor easy. It is painful. Hence, pressure your main character until he has not other choice but to face his fear and enter the forest. In other words: Hurt him. In agreement with @Standback's answer, you need to provide detail: Why is he scared to go into the forest in the first place? Similary, why should he go in there at all? Why not stay on the nice, sunny lawn surrounding the forest? There's food, there's light, everything is well. Unless, of course, the lawn is poisoned. Or the love interest of the main character is captured and held prisonder in the wood. Or a spectre stole his soul and hid it in the forest. And so on.
On a more serious note and in case you speak German, here is a brilliant but terrifying reportage on the fate of women that have been kidnapped by Boko Haram and held prisonders in Nigeria's Sambisa forest. (This is not for the faint of heart and I post it here for the sole purpose to illustrate what a forest can be. In the case of the reportage it is hell.)
Whatever you do, make sure that your main character has no other choice left but to enter the forest.
Concerning your sub-questions:
- To me, a believable development is one that happens gradually and is well-prepared. You need to give me the chance to the see the character evolve. Granting him a sudden epiphany on his nice, sunny lawn would not work for me. Similarly, being shown a caterpillar on one page and a butterfly on the next would not convince me. Show me the chrysalis inbetween and explain to me why the caterpillar had to pupate to survive.
- Character development is intrinsic to the approach sketched above. Inspiring sympathy however, is a different matter. Generally, I sympathize with characters that are in trouble. Again, by leaving your character no other choice but to enter the forest, you automatically create trouble. (Mind, creating a likable character is different from creating a character that your readers can sympathize with.)