there is a difference between the mails you send to a smtp server and from it.
As already said, sometimes there are some antispam blacklists which include the range of IP addresses of an ISP dedicated to home users and so they are classified as untrusted.
So if you, from your home connection, try to send a mail directly using the SMTP server of the recipient (that use these blackslists) is possible that you will be kicked.
Different is if you have the same domain of the SMTP server (for example
yourname@hotmail.com and you use the MX of hotmail) and want to send a mail to me, in which case there are no problems since you are a trusted user.
Another problem which can happen when people try to send a mail for the first time is the lack of the <> delimiters in the source/recipient mail addresses (mailf from and rcpt to), in fact using
yourname@example.com is wrong and you must use <yourname@example.com>