"I want a new pen."
Basically because ほしい is an adjective, as opposed to a verb. The を particle is used to indicate a direct object, typically followed by a verb. But Japanese typically doesn't use a verb in this case when expressing that you want an item, so you wouldn't use を because the item you want isn't acting as the direct object.
ほしい is an adjective so it does not have an object so it is incorrect to use を. が is used to represent the target of hope, preference and ability like ほしい, たい, 好き, きらい, できる
what's the difference between あたらしい and あらたな？
新しい(あたらしい) ペンが ほしいです。 新たな(あらたな)ペンが欲しいです。
I think 新（あら）た is used mainly for abstract nouns like 新たな時代（じだい） (new era) and 新たなペン seems a bit odd to me.