I am going to try and break this down, using a tumblr post as my baseline (original link to post is dead) as it starts with great points. This is more or less a starting point in addressing it, and certainly does not cover it all.
What I mean when I say “toxic monogamy culture”:
the normalization of jealousy as an indicator of love
Jealousy is itself a normal emotion and there is nothing wrong with being jealous, however, using it as a way to indicate just how much you love your partner(s) or how much your partner(s) love you is incredibly unhealthy. It implies that a partner is thing you possess and own, it removes trust in each other, it undermines or invalidates other factors or insecurities that may not have been communicated, and may create a fear to share or communicate with each other. Learning polyamory is very likely to include jealousy, as people are generally socialized for monogamy. It takes time to unpack and unlearn much of it, and one of the primary most pieces we face at first is the jealousy. Being able to work through it together, to communicate, to give each other validation and space, and to allow for exploration of each other alongside other potential partners is key. It can be counter-intuitive and counter-productive to place jealousy as a measurement of love in a polyamorous relationship.
the idea that a sufficiently intense love is enough to overcome any practical incompatibilities
Intense passion and love is a wonderful thing, but it is not a tool to use in order to ignore practical incompatibilities. Practical incompatibilities may refer to things that cause an obvious set of differences and/or clash between each other, such as: different political stances that are at the forefront, priorities in health and safety, willingness to make compromise, willingness to communicate, openness regarding past and/or potential partners, dealing with unhealthy and harmful relationships and/or friendships, etc. If a relationship is hurtful, toxic, or even dangerous, there is no point where an intense love trumps this. Recognizing that some situations may be unclear and/or even abusive, therefore a possible lack of awareness may be in play. The important thing to take away here is this: be honest with each other and yourselves, love is not a cure-all.
the idea that you should meet your partner’s every need, and if you don’t, either you’re inadequate or they’re too needy
Such an idea is completely counter-intuitive to everything that polyamory is and does (in my opinion). However, it is another one of those ideas so deeply embedded and learned. Openness, patience, communication, and exploration may help in unlearning this. Everyone has different needs and different levels of needs. In the same way, everyone has different capacities and abilities in meeting needs. One or multiple partners may very likely be unable to meet one person’s needs, and there is nothing wrong with that. This may be apparent in a potential or new partner, but it can even be something learned later in the relationship. Either way, a person is not inadequate for such nor is the other too needy.
the idea that a sufficiently intense love should cause you to cease to be attracted to anyone else
While this one may be obvious as a group of polyamory folks, it can be very easy to convince each other or ourselves that the relationship(s) we currently have are fueled by enough love that there is no way we could find anyone else attractive. This is one of those things that can blur into other forms of “toxic monogamy culture” as it is very easy to tell ourselves this one intense love may be all we need. And it is true that in the first flames, or while it is new, it is great and amazing and all we need. As time progresses, this may change, and finding out the relationship is not all you need or all the other needs can be something hurtful or difficult to become aware of or understand. Give each other the benefit that your love, as intense as it is or isn’t, is valid and beautiful - but that seeking further, or needing more, and finding a new attraction is just as valid.
the idea that commitment is synonymous with exclusivity
This idea varies depending on the type or form of poly dynamic a persons may have. A person can be in a committed relationship and still be available for more. A person may be in a relationship that isn’t committed and decide they aren’t currently available for more. It varies on a person’s needs and capacities.
the idea that marriage and children are the only valid teleological justifications for being committed to a relationship
The reality with this one is that any relationship can be committed or non-committal for any myriad of reasons. A marriage is not the be all nor the end all, and certainly is not the priority in seeking commitment. No one relationship is better or “more committed” than another because there is a marriage. In the same way, having children does not need to be the end goal, and having children does not mean commitment must then happen. Marriage and children are not boxes that predicate commitment.
the idea that your insecurities are always your partner’s responsibility to tip-toe around and never your responsibility to work on
This is a big one in polyamory! Openness, honesty, and, you guessed it, communication! All partners involved must be willing to talk with each other about their insecurities that are relevant to the current situation(s) or may become relevant. Recognizing that there is no set timeline or time frame for this, just that some things need to be worked on together as they become applicable and when partners involved are ready. Hiding your insecurities is more likely to do harm than good, and in the same way, expecting a partner to only tip-toe without *both* doing work is likely to be just as harmful or even more so.
the idea that your value to a partner is directly proportional to the amount of time and energy they spend on you, and it is in zero-sum competition with everything else they value in life
The reasons a partner may limit their time with you can vary immensely, and to limit the time spent with a person should not be seen as something inherently negative. A partner’s schedule may be incredibly busy, mental capacity and ability has a part, physical capacity and ability has a part, other commitments or projects may need their time, relationship dynamics and styles may vary, etc etc. Time spent is not mutually exclusive with the value of the relationship or the people involved. This is another big one that societal norms enforces, and it takes a lot of work and time for many of us to unpack and unlearn.
the idea that being of value to a partner should always make up a large chunk of how you value yourself
Only you know what is best for you, and no one else can decide that. You need to take care of you, and only you know what that means. So in the same way, your self-worth and value comes before any measurements of value that may come from a partner. For many of us in polyamory, we have all kinds of different relationships in different forms and to different extents. Some of us are solo, anarchy, or hierarchy - however that works for each of us does not directly define individual worth.