Analog gave you a comprehensive answer. In two words: IP reputation.
The takeaway is that not all IP addresses are equal in terms of reputation. If you send from a residential connection using a big, national ISP your delivery rate could suffer, given that the overall volume of spam recorded from that ISP is usually going to be somewhat significant. There is some kind of collective penalty. You suffer because of the actions of other customers.
That may vary a lot depending on source and destination. Every ISP or providers have their own lists and criteria to determine what qualifies as spam.
That being said, you can definitely send E-mail yourself. Make sure that you comply with applicable regulations, your subscribers should be opt-in and should be able to easily unsubscribe. If you fall within EU jurisdiction, you may have to consider compliance with GDPR.
Third-party services not only take care of the delivery, but they also take care of those legal and practical aspects - in simple terms they manage a database of subscribers for you.
My own experience: I manage a number of servers with dedicated IP addresses, some of which assigned for a very long time (> 10 years). In spite of this I have noticed that sometimes the IP addresses land in some blacklist (Spamhaus or other) for no real reason (I do not spam and hardly send any mail). The most likely reason is that sometimes they blacklist a block like a /24 or more, instead of a single IP address.
Some webhosts have a bad reputation because they are lenient on spam (or even cybercrime), they are more likely to be blacklisted by peers. If you have a bad host, expect to have poor delivery rates.
Note that even using dedicated IP addresses does not guarantee you won't have problems. They may have been used in the past, so they have history. And like I said above some blacklists are happy to ban in bulk rather than go for the surgical approach.
So when you are in some blacklist, you have to apply for delisiting, the process is often automated but not always. Sometimes you have to get hold of a real human for a manual review, who is not always sympathetic - they assume you are guilty.
Even mail servers from Google are blacklisted at times.
In conclusion, you can send the mail yourself but watch your logs. If you have many rejections, investigate them. Check if your IP addresses are in some blacklists by any chance and if they are, have them delisted.
They are some steps you can do to increase 'acceptance' rates like using DMARC, publish a SPF record or having a proper PTR record etc. To some extent, remote MTAs are more likely to trust your mail if it complies with standard practices. The keyword here is: scoring.
The thing is, sending E-mail has become a specialized trade just like web hosting is a specialized trade too. After all, anybody can set up a webserver and even host it at home but we agree that is usually not a professional solution. Until the mid-1990s spam was not a problem but since there is so much spam nowadays, all Internet actors have become more strict. As a result, even sending legitimate mail - and making sure it will get through to the recipient - is more difficult than it used to be.