The many upsides are well covered by other answers. However, businesses often do not open source their software for the following worries.
Please don't take this as a defense or being in favor of closed source. I'm simply the messenger.
Giving away competitive advantage
If your software does something remarkably different from your competitors, and you open source it, it will be easier for your competitor to copy the feature. Then there is one less reason to go with your product over a competitor. This is the same reason the Coke formula stays locked in a vault.
Loss of IP value
When your software is closed, the source and rights are assets that could be sold or licensed to another company. But if that company can get a copy of the same code and usage rights for free, it is much less valuable.
Loss of control
When you open source software, it is essentially no longer yours... especially if it becomes popular. It becomes harder to make changes as the number of stakeholders increases to internet scale. For example, Guido van Rossum stepping down.
Budgetary concerns
A lot of us readily ask for a lot of things in open source repos, and far fewer of us are willing or able to help. Having a constant influx of issues to triage and prioritize takes labor. Also, popular community requests may not be needed by your company. So open sourcing can add extra overhead cost to the budget.
AGPL as a corporate tactic
AGPL is often used by corps to prevent loss of competitive advantage and IP value while still enjoying the benefits of being open source. They release an open-source, community edition under AGPL. Since the AGPL has significant restrictions on usage, the license can be used as a big stick to prevent competitors from using the code to take competitive advantage. It also blocks the software from being used in commercial products. (By default, it cannot even be used by other open source products except GPLv3-licensed.) However, the corp still retains ownership rights which means they can choose to release the same code (or derivative) under a different license. So the corp also sells the software under a commercial license. Paying customers are therefore not entangled with the AGPL restrictions -- they can integrate it into proprietary products or make proprietary modifications to source without sharing.
Disclaimer: I am not a lawyer, just a keen observer.
Personally, I think that OSS is one of the great wonders of our field. I am simply exposing the worries that businesses have about open sourcing their software. It's why Microsoft doesn't open source Office; Apple doesn't open source Logic Pro; Google and Facebook don't open source their ad tech; etc. They might open source infrastructural bits and pieces, but not the core ones that make money or are vital to the business (e.g. Google's search ranking code).
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The many upsides are well covered by other answers. However, businesses often do not open source their software for the following worries.
Please don't take this as a defense or being in favor of closed source. I'm simply the messenger.
Giving away competitive advantage
If your software does something remarkably different from your competitors, and you open source it, it will be easier for your competitor to copy the feature. Then there is one less reason to go with your product over a competitor. This is the same reason the Coke formula stays locked in a vault.
Loss of IP value
When your software is closed, the source and rights are assets that could be sold or licensed to another company. But if that company can get a copy of the same code and usage rights for free, it is much less valuable.
Loss of control
When you open source software, it is essentially no longer yours... especially if it becomes popular. It becomes harder to make changes as the number of stakeholders increases to internet scale. For example, Guido van Rossum stepping down.
Budgetary concerns
A lot of us readily ask for a lot of things in open source repos, and far fewer of us are willing or able to help. Having a constant influx of issues to triage and prioritize takes labor. Also, popular community requests may not be needed by your company. So open sourcing can add extra overhead cost to the budget.
Personally, I think that OSS is one of the great wonders of our field. I am simply exposing the worries that businesses have about open sourcing their software. It's why Microsoft doesn't open source Office; Apple doesn't open source Logic Pro; Google and Facebook don't open source their ad tech; etc. They might open source infrastructural bits and pieces, but not the core ones that make money or are vital to the business (e.g. Google's search ranking code).