the first part says that either 「を」or「から」can be used for a sentence with 船, presumably an inanimate object, as the subject.
Word's animacy in Japanese
As you may know, nouns in Japanese has a category animacy, which is decided by whether the object is "sentient" or "animal-like", and affects verb choice and numerous grammatical phenomena. What should be noted is, however, that a noun is not always considered animate or inanimate by nature, but judged on a case-by-case basis.
A car cannot move by itself, but when a driver is in, it (as a whole) can travel freely as if has a will. Thus an attended car is animate. This is naturally true for all transportation and other manipulated moving machines (including those commanded by AI). To be more specific, judgment toward those objects of non-evident animacy relies much on the observer's attitude and expectation. For instance, even you can't see the driver clearly, a taxi coming down the street with "for hire" sign is probably animate; even it is moving, your car rolling because you have forgotten to set the parking brake is presumably inanimate; a dead body is inanimate, but it is safer to assume a lying corpse animate in a zombie outbreak; and so on.
In this case, a ship obviously piloted is animate.
～を出る vs ～から出る
Verbs that mean going out or leaving can have its place of origin marked by particle を or から. The difference is that with から, the place is imagined as a real location, with extent and boundary, while with を, it is more like a conceptual point than a physical place (like a station shown on a timetable or a route map). English also has a similar distinction that lets you say you are "at the airport" or "in the airport"; an airport is a big facility, but the former ignores the geospatial details and focuses on the fact that you are "functionally" at the point accessible to what it provides and not to what another place does, unlike the latter means you are somewhere in its premises.
As a result, ～を出る means that you "conceptually" leave the place, or to say, you go out of that place with a clear orientation (if not intent) toward elsewhere. ～から出る simply means out of the boundary, including when you accidentally put your foot one step out of the border. Thus in most cases, what can do ～を出る is something animate, but it is not a hard requirement. 銃口を飛び出した弾 "bullet discharged from the barrel" and 湖を出た川 "river flowed out of the lake" are perfectly normal, because they are directed by fixed courses. On the contrary, as the handbook says, 大学を出る "graduate from college" is only an abstract idea irrelevant with walking out of the campus site, so you can't replace it with ～から.