neglect vs leave out

neglect is a noun but leave out is not a noun.

Word	Noun	Adjective	Verb	Adverb
neglect	Yes	No	Yes	No
leave out	No	No	Yes	No

As verbs, neglect and leave out are synonyms defined as:

Other synonyms of neglect include drop, miss, omit, overleap, overlook, pretermit.

neglect (noun)	leave out (noun)
failure to act with the prudence that a reasonable person would exercise under the same circumstances
willful lack of care and attention
the trait of neglecting responsibilities and lacking concern
lack of attention and due care
the state of something that has been unused and neglected

neglect (verb)	leave out (verb)
leave undone or leave out	leave undone or leave out
give little or no attention to	prevent from being included or considered or accepted
fail to attend to
fail to do something; leave something undone