I am seeing someone who has told me they don't have the capacity or capability to be in love with me. They have never been in love, despite really trying in the past. Is not being in love a bad sign if I am looking for a life partner? Can I continue to pursue a relationship with them or am I setting myself up for failure and hurt down the road?
First, let me start by saying that I am going into the relationship advice presented in this response assuming your partner is treating you right, indicates they care for you in some capacity, and respect you at a base line.
I imagine it can be quite jarring to hear from your romantic partner that they are not in love with you and likely never will be. In a world where we expect our romantic relationships to look and feel a certain way, that can be a difficult thing to confront. I would first like to say that it is okay to feel what ever way you need to feel as you navigate this situation.
With relation to your questions, I pose three of my own.
To start, what does your partner mean when they say they can't love you?
Does your partner simply mean they can't feel a spark with you? Is it about an inability to form and nurture an emotional connection with you? Is it about an inability to adequately express affection toward you? Is it that they feel with you and for you, but can't or wont commit to you long term? It is important to understand exactly what they mean when they say this to you.
Sometimes, people feel that love must feel a particular way, but the reality is that love may look and feel different to different people, and that isn't necessarily a bad thing.
Next, how does your partner feel about their inability to love you--do they see this as a problem?
If your partner sees love as something they will never have, and they don't see it as an issue, then I would also not see it as an issue. From a research perspective, love isn't one size fits all. It will look and feel different for different people in different relationships. Sometimes, love is about an overwhelming and all-consuming feeling, other times it is a decision we make.
For example, Sternberg postulates that love is comprised of three qualities: intimacy, passion, and commitment. Intimacy referencing closeness, passion referencing sexual desire, and commitment reflecting an intentional dedication to the relationship. Relationships may only encompass one of these features, but can also be comprised of any two or all three of these qualities. Although we might strive for a consummate love that encompasses all three qualities, it is not unusual to have a love that primarily embodies one or two. For example, without feelings of sexual desire, you might only experience commitment and intimacy -- which is enough for a relationship to persist pretty happily. Some research finds that passion may be something that fluctuates over time, more so than intimacy or commitment.
Essentially, if your partner likes you and is committed to being in a relationship with you, research has found the presence of both to be associated with having a satisfying relationship.
On the other hand, if your partner sees this as something they could potentially find with someone else, and they are desperate to experience it, I would be a little more concerned. From my perspective, I would worry they would be waiting for the person they think they will be able to form that connection with.
It is possible that put into these terms, your partner may be experiencing love in a way that is different than they would expect love to be. A reframing of what love is to them may help them understand their thoughts and feelings in the relationship.
So, altogether, if they like you and want to be with you, and they aren't themselves all that bothered with love looking different for them, then I view this as a non-issue.
Second, Is it a problem for you that they may not have that traditional love experience with you?
Beyond your partner's perspective on love and what they want from a relationship, it is important to understand what you want to experience with your partner. Did you find the relationship fulfilling for you before your partner shared this revelation with you? Do you feel like something is missing from the relationship? Will it bother you to know that your partner doesn't think he is in love with you?
If you think this is something that will cause you to ruminate, meaning you will spend a great deal of time thinking about this issue, then it likely will contribute to relationship dissatisfaction. If you are able to reframe what this means from your partner and consider that love may look different for them and it isn't a bad thing, or a reflection on you, then you can make things work.
How can you move forward?
I would recommend having a conversation with your partner about this. Ask them what they mean when they say they aren't capable of love with you. This may be a difficult conversation to have, but it may help you make decisions about whether this relationship will work for you.
Here are some example talking points:
What do they imagine love looks and feels like? What do they feel is missing with you?
Does this bother them?
They indicated they have desperately tried to love someone in the past - are they still searching for those feelings?
The bottom line is, a lack of consummate love isn't inherently a problem. It definitely doesn't have to mean the relationship will be doomed. But, it is important to reflect on what you want out of your partnership, and whether you are likely to feel less than you want to in a relationship where your partner feels a lack of love. If this person respects you, is committed to you, and treats you the way you'd like to be treated - that is just fine.
References
Sternberg, R. J. (1986). A triangular theory of love. Psychological Review, 93(2), 119–135. https://doi.org/10.1037/0033-295X.93.2.119
Madey, S. F., & Rodgers, L. (2009). The Effect of Attachment and Sternberg's Triangular Theory of Love on Relationship Satisfaction. Individual Differences Research, 7(2).