は can be used to describe the general feature of something, while が does not have such a nuance.
- りんごは赤い。 Apples are red. (as the general fact)
- りんごが赤い。 This (specific) apple looks red.
- 鳥は飛ぶ。 Birds (can) fly. (as the general fact)
- 鳥が飛んでいる。 A (certain) bird is flying.
Let's take a look at the third stanza. See that いま is always used with が? Here, the poet is not trying to explain the general facts about something. He is saying a certain soldier is wounded somewhere in this moment, a certain dog is now barking somewhere, the earth is now rotating, etc. 「いま兵士は傷つく」 sounds odd because he has not introduced any soldier into "the universe of discourse" before that line, and a soldier is not something that is always wounded.
In the final stanza, the poet is presenting 鳥ははばたく, 人は愛する, etc., as the general facts which are always true.
In other words, the third stanza is saying "Many things are now randomly happening in this world, and that is what 生きる means." The final stanza is saying something more abstract and philosophical... "Every truth in this world is 生きる" or something like that.