Historically, the phrase All rights reserved was used to reserve, or hold for one's own use, a copyright. The Buenos Aires Convention in 1910 required the use of that phrase for the purposes of establishing a copyright. At that time, there wasn't as much of a need to distinguish between ownership and license. Book publishing houses purchased manuscripts from authors and wanted to prevent rogue printing houses from selling pirated (physical) copies to the public. In that time in history, an iron-clad denial of license combined with a copyright claim was desirable and became the norm. The Buenos Aires Convention could not have anticipated the complexities of modern software licensing.
Today, the phrase All rights reserved is 100% globally obsolete for the purposes of establishing copyright but continues to be used due to convention alone. While the phrase makes little difference in situations where no license is granted (other than to perhaps make it very clear no license is granted), the phrase can make a tremendous difference in a license agreement that expressly grants certain rights.
To emphasize my previous point: Many people argue using the phrase All rights reserved has no meaning since it is obsolete for the purposes retaining copyright. They are correct on that point. However, what these people fail to realize is there is a difference between ownership of copyright and exercising that copyright through licensing of a work. While the words All rights reserved may have no meaning in terms of retaining ownership, they certainly can and do have a lot of meaning in terms of licensing. The words "all," "rights," and "reserved" do not stop having meaning in a license agreement just because they have no meaning in establishing copyright.
To reserve all rights implies you refuse to license any right. You are saying, "this is mine, you cannot do anything with it." It becomes contradictory then if in the next sentence you start talking about what someone can actually do. The phrase All rights reserved in a license creates ambiguity which is not good to have in a license agreement.
Commercial software often has phrases to the effect of "all rights reserved except as delineated below" to reserve all rights except those expressly provided in a license.
Where the Problem Began
The phrase All rights reserved in open source licensing originated in the BSD license created by the Regents of the University of California who wanted a way to license the Berkeley Software Distribution. Their attorneys had to work under duress because there were tremendous legal conflicts at the time related to Unix and they needed a license that would satisfy the many stakeholders involved in the disputes while keeping the University of California system out of legal trouble. I believe that in their haste, they added the phrase All rights reserved without considering the meaning of those words in a license agreement. They may have also just been following decades-old convention that preceded software licensing without considering its impact on a software license.
This Problem Mainly Exists in the BSD Licenses
Luckily, other than the BSD license (and Apple's derivative), no other major open source license includes the phrase All rights reserved. I've taken the time to prove this with the following list that includes a link to each license.
Does the open source license include the phrase All rights reserved?
As you can see, it is very uncommon to include the phrase All rights reserved in the context of open source software licensing. In fact, the Boost Software License (BSL) FAQ goes as far as to expressly forbids using the phrase All rights reserved.
The MIT License Does Not Include All rights reserved.
Specific to the OP's question, this is the actual MIT license:
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
The MIT License beings at the copyright line, not after it. The license allows for the insertion of
<copyright holders>, and nothing else. If someone inserts the (contradictory) clause All rights reserved, you are no longer dealing with the MIT License but a variant. It would not be fair to call a license with the words
All rights reserved the MIT License. The MIT License has built up trust and credibility over decades and that cannot be extended to a variant that reserves all rights in contradiction to the rest of the license.
Maybe We Should Say "Some Rights Reserved."
Creative Commons took an interesting approach with their old slogan Some rights reserved. While this is certainly not part of any Creative Commons license, their explanation of the idea explains the dilemma they were trying to solve:
Copyright grants to creators a bundle of exclusive rights over their creative works, which generally include, at a minimum, the right to reproduce, distribute, display, and make adaptations. The phrase "All Rights Reserved" is often used by owners to indicate that they reserve all of the rights granted to them under the law. When copyright expires, the work enters the public domain, and the rights holder can no longer stop others from engaging in those activities under copyright, with the exception of moral rights reserved to creators in some jurisdictions. Creative Commons licenses offer creators a spectrum of choices between retaining all rights and relinquishing all rights (public domain), an approach we call "Some Rights Reserved."
Stop Trying to Justify All rights reserved.
All rights reserved is a historic relic that is not relevant today for establishing copyright (the ownership part). In terms of licensing, it is detrimental to modern software licensing. The phrase has very specific, absolute meaning in the English language and can open up ambiguity in software licensing if it contradicts the rest of a license.
Personally, I suggest using the actual MIT License or my personal favorite, the ISC License, as is used by the OpenBSD project and others. All rights reserved should have never made it into a major open source license and rather than continuing its use, we need to break from the now-incorrect tradition.